Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C53×#359 ⋊ C2 |
| Sylow | C53 ⋊ #13392 |
386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(54,57,58,74,60,76,80,77)(55,62,63,89,65,91,78,90)(56,67,68,98,71,73,70,103)(59,83,79,109,84,110,112,75)(61,85,66,95,87,115,88,117)(64,93,81,106,94,105,111,72)(69,101,100,99,82,113,102,108)(86,107,96,114,92,97,116,104);(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)(55,61)(57,73)(58,70)(59,82)(60,71)(62,85)(63,88)(64,92)(65,87)(66,78)(67,76)(68,80)(69,84)(72,104)(74,98)(75,99)(77,103)(79,100)(81,96)(83,101)(86,94)(89,117)(90,95)(91,115)(93,97)(102,112)(105,107)(106,114)(108,109)(110,113)(111,116);(54,55)(56,66)(57,72)(58,78)(59,81)(60,65)(61,68)(62,75)(63,80)(64,79)(67,97)(69,86)(70,87)(71,88)(73,107)(74,105)(76,106)(77,93)(82,92)(83,90)(84,111)(85,113)(89,110)(91,109)(94,112)(95,99)(96,102)(98,114)(100,116)(101,115)(103,104)(108,117)Polycyclic presentation:
2^8,53|c^2=d,d^2=h,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,f^a=fh,g^a=gh,c^b=cf,d^b=dh,e^b=eh,i^b=i^52,e^c=egh,f^c=fh,g^c=gh,i^c=i^521184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88806);