Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #33458 |
646 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 121 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(59,67)(61,75)(65,86)(68,91)(69,83)(70,96)(71,97)(76,103)(77,104)(78,94)(87,93)(92,102)(98,118)(99,109)(106,121)(107,119);(54,56,57,55)(58,61,64,75)(59,66,67,90)(60,71,74,97)(62,76,82,103)(63,77,80,104)(65,85,86,112)(68,88,91,114)(69,89,83,108)(70,95,96,117)(72,98,101,118)(73,99,84,109)(78,105,94,116)(79,106,110,121)(81,107,100,119)(87,111,93,115)(92,113,102,120);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(58,60,64,74)(59,65,67,86)(61,71,75,97)(62,79,82,110)(63,84,80,73)(66,85,90,112)(68,92,91,102)(69,93,83,87)(70,94,96,78)(72,100,101,81)(76,106,103,121)(77,109,104,99)(88,113,114,120)(89,115,108,111)(95,116,117,105)(98,119,118,107);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55,57,56)(58,59)(60,70)(61,66)(62,78)(63,83)(64,67)(65,72)(68,81)(69,80)(71,95)(73,102)(74,96)(75,90)(76,105)(77,108)(79,93)(82,94)(84,92)(85,98)(86,101)(87,110)(88,107)(89,104)(91,100)(97,117)(99,120)(103,116)(106,115)(109,113)(111,121)(112,118)(114,119)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,c^2=fh,e^2=gh,g^2=h,b^a=be,d^a=dh,e^a=eg,g^a=gh,i^a=i^52,e^b=eg,g^b=gh,i^b=i^52,d^c=dh2144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322947);