Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C22 |
| direct product | C53×#10461 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C53 |
| prime radical | C22×D4×C53 | D4 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
406 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 77 points:
(1,2,3,5)(4,6,8,7)(9,10,13,17)(11,18,19,22)(12,14,20,16)(15,23,24,21)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77);(2,5)(6,7)(10,14)(11,19)(12,20)(15,22)(16,17)(18,24);(2,6)(4,8)(5,7)(9,11,20,23,13,19,12,21)(10,15,14,22,17,24,16,18)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 3449);