Finite Group Databasebeta

← Group #4325

Character table — Group #4325

Order 176.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32
size11222222222224444444444444444222244
order124111111111122222222224444444444444444444444444444444882
χ111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1
χ31111111111111-111111-1-1-1-1-1-1-1-1-1-111-1
χ41111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-11
χ5222−ζ36−ζ52−ζ12−ζ76−ζ28−ζ60−ζ20−ζ68−ζ4−ζ84−ζ36−ζ52−ζ12−ζ76−ζ28−ζ60−ζ20−ζ68−ζ4−ζ842−ζ36−ζ52−ζ12−ζ76−ζ28−ζ60−ζ20−ζ68−ζ4−ζ84−ζ36−ζ52−ζ36−ζ52−ζ12−ζ76−ζ12−ζ76−ζ28−ζ60−ζ28−ζ60−ζ20−ζ68−ζ20−ζ68−ζ4−ζ84−ζ4−ζ84000
χ6222−ζ36−ζ52−ζ12−ζ76−ζ28−ζ60−ζ20−ζ68−ζ4−ζ84−ζ36−ζ52−ζ12−ζ76−ζ28−ζ60−ζ20−ζ68−ζ4−ζ84-2−ζ36−ζ52−ζ12−ζ76−ζ28−ζ60−ζ20−ζ68−ζ4−ζ84ζ36+ζ52ζ36+ζ52ζ12+ζ76ζ12+ζ76ζ28+ζ60ζ28+ζ60ζ20+ζ68ζ20+ζ68ζ4+ζ84ζ4+ζ84000
χ7222−ζ12−ζ76−ζ4−ζ84−ζ20−ζ68−ζ36−ζ52−ζ28−ζ60−ζ12−ζ76−ζ4−ζ84−ζ20−ζ68−ζ36−ζ52−ζ28−ζ602−ζ12−ζ76−ζ4−ζ84−ζ20−ζ68−ζ36−ζ52−ζ28−ζ60−ζ12−ζ76−ζ12−ζ76−ζ4−ζ84−ζ4−ζ84−ζ20−ζ68−ζ20−ζ68−ζ36−ζ52−ζ36−ζ52−ζ28−ζ60−ζ28−ζ60000
χ8222−ζ12−ζ76−ζ4−ζ84−ζ20−ζ68−ζ36−ζ52−ζ28−ζ60−ζ12−ζ76−ζ4−ζ84−ζ20−ζ68−ζ36−ζ52−ζ28−ζ60-2−ζ12−ζ76−ζ4−ζ84−ζ20−ζ68−ζ36−ζ52−ζ28−ζ60ζ12+ζ76ζ12+ζ76ζ4+ζ84ζ4+ζ84ζ20+ζ68ζ20+ζ68ζ36+ζ52ζ36+ζ52ζ28+ζ60ζ28+ζ60000
χ9222−ζ28−ζ60−ζ20−ζ68−ζ12−ζ76−ζ4−ζ84−ζ36−ζ52−ζ28−ζ60−ζ20−ζ68−ζ12−ζ76−ζ4−ζ84−ζ36−ζ522−ζ28−ζ60−ζ20−ζ68−ζ12−ζ76−ζ4−ζ84−ζ36−ζ52−ζ28−ζ60−ζ28−ζ60−ζ20−ζ68−ζ20−ζ68−ζ12−ζ76−ζ12−ζ76−ζ4−ζ84−ζ4−ζ84−ζ36−ζ52−ζ36−ζ52000
χ10222−ζ28−ζ60−ζ20−ζ68−ζ12−ζ76−ζ4−ζ84−ζ36−ζ52−ζ28−ζ60−ζ20−ζ68−ζ12−ζ76−ζ4−ζ84−ζ36−ζ52-2−ζ28−ζ60−ζ20−ζ68−ζ12−ζ76−ζ4−ζ84−ζ36−ζ52ζ28+ζ60ζ28+ζ60ζ20+ζ68ζ20+ζ68ζ12+ζ76ζ12+ζ76ζ4+ζ84ζ4+ζ84ζ36+ζ52ζ36+ζ52000
χ11222−ζ20−ζ68−ζ36−ζ52−ζ4−ζ84−ζ28−ζ60−ζ12−ζ76−ζ20−ζ68−ζ36−ζ52−ζ4−ζ84−ζ28−ζ60−ζ12−ζ762−ζ20−ζ68−ζ36−ζ52−ζ4−ζ84−ζ28−ζ60−ζ12−ζ76−ζ20−ζ68−ζ20−ζ68−ζ36−ζ52−ζ36−ζ52−ζ4−ζ84−ζ4−ζ84−ζ28−ζ60−ζ28−ζ60−ζ12−ζ76−ζ12−ζ76000
χ12222−ζ20−ζ68−ζ36−ζ52−ζ4−ζ84−ζ28−ζ60−ζ12−ζ76−ζ20−ζ68−ζ36−ζ52−ζ4−ζ84−ζ28−ζ60−ζ12−ζ76-2−ζ20−ζ68−ζ36−ζ52−ζ4−ζ84−ζ28−ζ60−ζ12−ζ76ζ20+ζ68ζ20+ζ68ζ36+ζ52ζ36+ζ52ζ4+ζ84ζ4+ζ84ζ28+ζ60ζ28+ζ60ζ12+ζ76ζ12+ζ76000
χ13222−ζ4−ζ84−ζ28−ζ60−ζ36−ζ52−ζ12−ζ76−ζ20−ζ68−ζ4−ζ84−ζ28−ζ60−ζ36−ζ52−ζ12−ζ76−ζ20−ζ682−ζ4−ζ84−ζ28−ζ60−ζ36−ζ52−ζ12−ζ76−ζ20−ζ68−ζ4−ζ84−ζ4−ζ84−ζ28−ζ60−ζ28−ζ60−ζ36−ζ52−ζ36−ζ52−ζ12−ζ76−ζ12−ζ76−ζ20−ζ68−ζ20−ζ68000
χ14222−ζ4−ζ84−ζ28−ζ60−ζ36−ζ52−ζ12−ζ76−ζ20−ζ68−ζ4−ζ84−ζ28−ζ60−ζ36−ζ52−ζ12−ζ76−ζ20−ζ68-2−ζ4−ζ84−ζ28−ζ60−ζ36−ζ52−ζ12−ζ76−ζ20−ζ68ζ4+ζ84ζ4+ζ84ζ28+ζ60ζ28+ζ60ζ36+ζ52ζ36+ζ52ζ12+ζ76ζ12+ζ76ζ20+ζ68ζ20+ζ68000
χ1522-222222222220-2-2-2-2-20000000000000
χ1622-2−ζ36−ζ52−ζ12−ζ76−ζ28−ζ60−ζ20−ζ68−ζ4−ζ84−ζ36−ζ52−ζ12−ζ76−ζ28−ζ60−ζ20−ζ68−ζ4−ζ840ζ36+ζ52ζ12+ζ76ζ28+ζ60ζ20+ζ68ζ4+ζ84ζ36−ζ52−ζ36+ζ52ζ12−ζ76−ζ12+ζ76ζ28−ζ60−ζ28+ζ60ζ20−ζ68−ζ20+ζ68−ζ4+ζ84ζ4−ζ84000
χ1722-2−ζ36−ζ52−ζ12−ζ76−ζ28−ζ60−ζ20−ζ68−ζ4−ζ84−ζ36−ζ52−ζ12−ζ76−ζ28−ζ60−ζ20−ζ68−ζ4−ζ840ζ36+ζ52ζ12+ζ76ζ28+ζ60ζ20+ζ68ζ4+ζ84−ζ36+ζ52ζ36−ζ52−ζ12+ζ76ζ12−ζ76−ζ28+ζ60ζ28−ζ60−ζ20+ζ68ζ20−ζ68ζ4−ζ84−ζ4+ζ84000
χ1822-2−ζ12−ζ76−ζ4−ζ84−ζ20−ζ68−ζ36−ζ52−ζ28−ζ60−ζ12−ζ76−ζ4−ζ84−ζ20−ζ68−ζ36−ζ52−ζ28−ζ600ζ12+ζ76ζ4+ζ84ζ20+ζ68ζ36+ζ52ζ28+ζ60ζ12−ζ76−ζ12+ζ76ζ4−ζ84−ζ4+ζ84−ζ20+ζ68ζ20−ζ68ζ36−ζ52−ζ36+ζ52ζ28−ζ60−ζ28+ζ60000
χ1922-2−ζ12−ζ76−ζ4−ζ84−ζ20−ζ68−ζ36−ζ52−ζ28−ζ60−ζ12−ζ76−ζ4−ζ84−ζ20−ζ68−ζ36−ζ52−ζ28−ζ600ζ12+ζ76ζ4+ζ84ζ20+ζ68ζ36+ζ52ζ28+ζ60−ζ12+ζ76ζ12−ζ76−ζ4+ζ84ζ4−ζ84ζ20−ζ68−ζ20+ζ68−ζ36+ζ52ζ36−ζ52−ζ28+ζ60ζ28−ζ60000
χ2022-2−ζ28−ζ60−ζ20−ζ68−ζ12−ζ76−ζ4−ζ84−ζ36−ζ52−ζ28−ζ60−ζ20−ζ68−ζ12−ζ76−ζ4−ζ84−ζ36−ζ520ζ28+ζ60ζ20+ζ68ζ12+ζ76ζ4+ζ84ζ36+ζ52ζ28−ζ60−ζ28+ζ60−ζ20+ζ68ζ20−ζ68ζ12−ζ76−ζ12+ζ76−ζ4+ζ84ζ4−ζ84ζ36−ζ52−ζ36+ζ52000
χ2122-2−ζ28−ζ60−ζ20−ζ68−ζ12−ζ76−ζ4−ζ84−ζ36−ζ52−ζ28−ζ60−ζ20−ζ68−ζ12−ζ76−ζ4−ζ84−ζ36−ζ520ζ28+ζ60ζ20+ζ68ζ12+ζ76ζ4+ζ84ζ36+ζ52−ζ28+ζ60ζ28−ζ60ζ20−ζ68−ζ20+ζ68−ζ12+ζ76ζ12−ζ76ζ4−ζ84−ζ4+ζ84−ζ36+ζ52ζ36−ζ52000
χ2222-2−ζ20−ζ68−ζ36−ζ52−ζ4−ζ84−ζ28−ζ60−ζ12−ζ76−ζ20−ζ68−ζ36−ζ52−ζ4−ζ84−ζ28−ζ60−ζ12−ζ760ζ20+ζ68ζ36+ζ52ζ4+ζ84ζ28+ζ60ζ12+ζ76ζ20−ζ68−ζ20+ζ68ζ36−ζ52−ζ36+ζ52−ζ4+ζ84ζ4−ζ84−ζ28+ζ60ζ28−ζ60−ζ12+ζ76ζ12−ζ76000
χ2322-2−ζ20−ζ68−ζ36−ζ52−ζ4−ζ84−ζ28−ζ60−ζ12−ζ76−ζ20−ζ68−ζ36−ζ52−ζ4−ζ84−ζ28−ζ60−ζ12−ζ760ζ20+ζ68ζ36+ζ52ζ4+ζ84ζ28+ζ60ζ12+ζ76−ζ20+ζ68ζ20−ζ68−ζ36+ζ52ζ36−ζ52ζ4−ζ84−ζ4+ζ84ζ28−ζ60−ζ28+ζ60ζ12−ζ76−ζ12+ζ76000
χ2422-2−ζ4−ζ84−ζ28−ζ60−ζ36−ζ52−ζ12−ζ76−ζ20−ζ68−ζ4−ζ84−ζ28−ζ60−ζ36−ζ52−ζ12−ζ76−ζ20−ζ680ζ4+ζ84ζ28+ζ60ζ36+ζ52ζ12+ζ76ζ20+ζ68−ζ4+ζ84ζ4−ζ84ζ28−ζ60−ζ28+ζ60ζ36−ζ52−ζ36+ζ52−ζ12+ζ76ζ12−ζ76ζ20−ζ68−ζ20+ζ68000
χ2522-2−ζ4−ζ84−ζ28−ζ60−ζ36−ζ52−ζ12−ζ76−ζ20−ζ68−ζ4−ζ84−ζ28−ζ60−ζ36−ζ52−ζ12−ζ76−ζ20−ζ680ζ4+ζ84ζ28+ζ60ζ36+ζ52ζ12+ζ76ζ20+ζ68ζ4−ζ84−ζ4+ζ84−ζ28+ζ60ζ28−ζ60−ζ36+ζ52ζ36−ζ52ζ12−ζ76−ζ12+ζ76−ζ20+ζ68ζ20−ζ68000
χ262-2022222-2-2-2-2-20000000000000000i2−i20
χ272-2022222-2-2-2-2-20000000000000000−i2i20
χ284-40−2ζ36−2ζ52−2ζ12−2ζ76−2ζ28−2ζ60−2ζ20−2ζ68−2ζ4−2ζ842ζ36+2ζ522ζ12+2ζ762ζ28+2ζ602ζ20+2ζ682ζ4+2ζ840000000000000000000
χ294-40−2ζ12−2ζ76−2ζ4−2ζ84−2ζ20−2ζ68−2ζ36−2ζ52−2ζ28−2ζ602ζ12+2ζ762ζ4+2ζ842ζ20+2ζ682ζ36+2ζ522ζ28+2ζ600000000000000000000
χ304-40−2ζ28−2ζ60−2ζ20−2ζ68−2ζ12−2ζ76−2ζ4−2ζ84−2ζ36−2ζ522ζ28+2ζ602ζ20+2ζ682ζ12+2ζ762ζ4+2ζ842ζ36+2ζ520000000000000000000
χ314-40−2ζ20−2ζ68−2ζ36−2ζ52−2ζ4−2ζ84−2ζ28−2ζ60−2ζ12−2ζ762ζ20+2ζ682ζ36+2ζ522ζ4+2ζ842ζ28+2ζ602ζ12+2ζ760000000000000000000
χ324-40−2ζ4−2ζ84−2ζ28−2ζ60−2ζ36−2ζ52−2ζ12−2ζ76−2ζ20−2ζ682ζ4+2ζ842ζ28+2ζ602ζ36+2ζ522ζ12+2ζ762ζ20+2ζ680000000000000000000

Here ζ is a primitive root of unity of order 88 (ζ88 = 1); i = ζ22.