Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C28 |
| direct product | C53×#61224 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C53 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C53×#532 ◁ G | |
2020 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 5 generators on 93 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,16)(12,22)(13,26)(14,29)(15,19)(17,20)(18,28)(21,34)(23,33)(24,38)(25,30)(27,31)(32,37)(35,40)(36,39)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3)(2,5)(4,8)(6,7)(9,11,15,14)(10,16,19,29)(12,23,25,20)(13,27,28,21)(17,22,33,30)(18,34,26,31)(24,35,39,37)(32,38,40,36);(9,12,15,25)(10,17,19,33)(11,20,14,23)(13,24,28,39)(16,30,29,22)(18,32,26,40)(21,35,27,37)(31,38,34,36);(3,8)(5,7)(13,28)(18,26)(21,27)(24,39)(31,34)(32,40)(35,37)(36,38);(9,13,15,28)(10,18,19,26)(11,21,14,27)(12,24,25,39)(16,31,29,34)(17,32,33,40)(20,35,23,37)(22,36,30,38)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 54212);