Finite Group Databasebeta

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C24×C32×C4×C5×C11 #72208432

order31680
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 19818086400
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210×C3

Aliases

abelianC24×C32×C4×C5×C11
multiplicative(ℤ/69069)ˣ, (ℤ/74152)ˣ, (ℤ/74865)ˣ, (ℤ/76648)ˣ, (ℤ/77385)ˣ, (ℤ/78568)ˣ, (ℤ/79695)ˣ, (ℤ/79856)ˣ, (ℤ/82544)ˣ, (ℤ/83080)ˣ, (ℤ/88088)ˣ, (ℤ/92092)ˣ, (ℤ/92680)ˣ, (ℤ/93800)ˣ, (ℤ/98088)ˣ, (ℤ/99696)ˣ, (ℤ/99820)ˣ, (ℤ/101016)ˣ, (ℤ/102672)ˣ, (ℤ/103180)ˣ, (ℤ/103272)ˣ, (ℤ/106128)ˣ, (ℤ/111048)ˣ, (ℤ/111216)ˣ, (ℤ/111228)ˣ, (ℤ/113256)ˣ, (ℤ/114972)ˣ, (ℤ/117852)ˣ, (ℤ/118404)ˣ, (ℤ/119160)ˣ, (ℤ/120600)ˣ, (ℤ/121968)ˣ, (ℤ/124620)ˣ, (ℤ/128340)ˣ, (ℤ/132132)ˣ, (ℤ/132660)ˣ, (ℤ/138138)ˣ, (ℤ/139020)ˣ, (ℤ/140700)ˣ, (ℤ/144900)ˣ, (ℤ/149730)ˣ, (ℤ/152460)ˣ, (ℤ/154770)ˣ, (ℤ/159390)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C25×C32×C5×C11
socle, prime radicalC25×C32×C5×C11C2
LCSG ▷ C1
UCSC1 ◁ G

16344 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

31680 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.