Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #12911 |
266 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 117 points:
(1,2)(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)(54,57)(55,63,66,87)(56,68)(58,74)(59,75)(60,77)(61,76)(62,83,85,111)(64,86,88,104)(65,73,82,103)(67,89,91,112)(69,93)(70,94)(71,96)(72,95)(78,102,108,117)(79,105)(80,107)(81,106)(84,101,109,114)(90,92,100,113)(97,110)(98,116)(99,115);(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)(54,56,58,69,60,72,80,99,61,71,81,98,59,70,79,97)(55,62,64,67,65,84,78,90,66,85,88,91,82,109,108,100)(57,68,74,93,77,95,107,115,76,96,106,116,75,94,105,110)(63,83,86,89,73,101,102,92,87,111,104,112,103,114,117,113);(54,55)(56,67,71,91)(57,73,76,103)(58,78)(59,65)(60,82)(61,66)(62,69,85,98)(63,75,87,77)(64,80)(68,92)(70,90,72,100)(74,104,106,86)(79,88)(81,108)(83,110)(84,97,109,99)(89,95)(93,114)(94,112)(96,113)(101,116)(102,105,117,107)(111,115)Polycyclic presentation:
2^8,53|a^2=f,b^2=d,c^2=eg,d^2=g,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,f^b=fh,i^b=i^52,f^c=fh,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, 86023);