Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C22×Q32×C53 ⋊ C2 |
| Sylow | C53 ⋊ #33721 |
794 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)(61,76)(66,87)(72,98)(77,103)(78,104)(84,110)(88,112)(89,106)(92,114)(97,113)(99,108)(100,118)(105,120)(111,115)(116,119)(117,121);(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)(54,55,56,57)(58,61)(59,66)(60,72)(62,77)(63,78)(64,76)(65,84)(67,88)(68,89)(69,87)(70,92)(71,97)(73,99)(74,100)(75,98)(79,105)(80,104)(81,103)(82,106)(83,108)(85,111)(86,110)(90,113)(91,112)(93,115)(94,116)(95,114)(96,117)(101,118)(102,119)(107,120)(109,121);(58,60,71,96,63,74,81,83,64,75,90,109,80,101,62,73)(59,65,79,94,68,85,91,95,69,86,107,102,82,93,67,70)(61,72,97,117,78,100,103,108,76,98,113,121,104,118,77,99)(66,84,105,116,89,111,112,114,87,110,120,119,106,115,88,92);(55,57)(58,59,64,69)(60,70,75,95)(61,66,76,87)(62,79,81,107)(63,82,80,68)(65,83,86,73)(67,90,91,71)(72,92,98,114)(74,102,101,94)(77,105,103,120)(78,106,104,89)(84,108,110,99)(85,96,93,109)(88,113,112,97)(100,119,118,116)(111,117,115,121)Polycyclic presentation:
2^8,53|a^2=h,b^2=eg,c^2=f,e^2=gh,g^2=h,b^a=be,c^a=cf,e^a=eg,g^a=gh,d^c=dh,i^c=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 325024);