Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24404 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C24×C4 |
| direct product | C53×#25949 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C53 |
| prime radical | C2×#120×C53 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C23×C4×C53 ◁ G | |
1202 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 77 points:
(1,2,5,7)(3,8,4,6)(9,10,13,16)(11,17,19,14)(12,15,21,23)(18,22,20,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77);(1,3,5,4)(2,6,7,8)(9,11,13,19)(10,14,16,17)(12,20,21,18)(15,22,23,24);(2,7)(6,8)(9,12,13,21)(10,15,16,23)(11,18)(14,22)(17,24)(19,20);(1,4,5,3)(2,8,7,6)(10,16)(14,17)(15,23)(22,24)2279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 18937);