Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C53×#510 ⋊ C2 |
| Sylow | C53 ⋊ #13335 |
536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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:
(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)(54,57)(55,62)(56,67)(58,78)(59,84)(60,75)(61,85)(63,93)(64,90)(65,96)(66,98)(68,105)(69,108)(70,103)(71,76)(72,104)(73,80)(74,79)(77,101)(81,111)(82,91)(83,102)(86,88)(87,117)(89,97)(92,115)(94,112)(95,116)(99,109)(100,113)(106,110)(107,114);(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)(54,56,60,70)(55,61,64,86)(57,67,75,103)(58,77,81,113)(59,83,79,69)(62,88,90,85)(63,92,94,107)(65,95,82,87)(66,97,99,76)(68,104,106,80)(71,109,89,98)(72,110,73,105)(74,108,84,102)(78,101,111,100)(91,116,96,117)(93,114,112,115);(54,55)(56,66)(57,71)(58,76)(59,82)(60,64)(61,68)(62,73)(63,80)(65,79)(67,85)(69,107)(70,99)(72,90)(74,112)(75,89)(77,95)(78,96)(81,97)(83,92)(84,93)(86,106)(87,113)(88,103)(91,111)(94,104)(98,101)(100,109)(102,117)(105,115)(108,116)(110,114)Polycyclic presentation:
2^8,53|b^2=h,d^2=gh,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fh,g^a=gh,c^b=cf,d^b=dg,e^b=eg,g^b=gh,d^c=dgh,e^c=eg,g^c=gh,i^c=i^52866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88455);