Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #12684 |
894 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 199 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:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,57)(55,62)(56,66)(58,71)(59,72)(60,70)(61,76)(63,81)(64,82)(65,80)(67,87)(68,88)(69,89)(73,95)(74,93)(75,94)(77,86)(78,98)(79,99)(83,105)(84,103)(85,104)(90,97)(91,109)(92,110)(96,112)(100,107)(101,108)(102,114)(106,116)(111,113)(115,117);(54,56)(55,61)(57,66)(58,68)(59,69)(60,67)(62,76)(63,78)(64,79)(65,77)(70,87)(71,88)(72,89)(73,92)(74,90)(75,91)(80,86)(81,98)(82,99)(83,102)(84,100)(85,101)(93,97)(94,109)(95,110)(96,111)(103,107)(104,108)(105,114)(106,115)(112,113)(116,117);(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)(54,55,58,63,59,64,73,83,60,65,74,84,75,85,96,106)(56,61,68,78,69,79,92,102,67,77,90,100,91,101,111,115)(57,62,71,81,72,82,95,105,70,80,93,103,94,104,112,116)(66,86,88,107,89,108,110,117,87,76,97,98,109,99,113,114)Polycyclic presentation:
2^8,53|a^2=f,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^52,e^b=eh,d^c=dh1832 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85016);