Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C26 |
| direct product | C53×#24402 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C23×C4×C53 ◁ G | |
1358 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 73 points:
(1,2)(3,4)(5,6,9,14,10,8,11,13)(7,15,17,20,18,12,19,16)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73);(2,4)(5,7)(6,12)(8,15)(9,17)(10,18)(11,19)(13,20)(14,16);(5,8)(6,10)(7,16)(9,14)(11,13)(12,17)(15,19)(18,20);(2,4)(5,9,10,11)(6,13,8,14)(7,17,18,19)(12,20,15,16)2279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 17390);