Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C53 · Schur multiplier (H2) = C27 |
| direct product | C2×C53×#1884 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C53 | #120 |
| commutator | C2×C4 | C23×C4×C53 |
| Frattini, cosocle | C22×C4 | C24×C53 |
| socle | C22×C53 | #386 |
| prime radical | C2×C53×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C53 ◁ C23×C4×C53 ◁ G | |
1794 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 71 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71);(3,4)(5,13,16,17)(6,10,9,15)(7,11)(8,12)(14,18);(3,5,7,10,8,16,18,15)(4,9,11,17,12,6,14,13);(3,6)(4,10)(5,14)(7,13)(8,9)(11,16)(12,15)(17,18)3392 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 13934);