Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16×C53 · Schur multiplier (H2) = C23 |
| direct product | C2×C53×#1400 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C53 | C22⋊C4 |
| commutator | C22 | C22×C16×C53 |
| Frattini, cosocle | C2×C16 | C23×C53 |
| socle | C22×C53 | C22⋊C16 |
| prime radical | C24×C53 | C16 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C53 ◁ C22×C16×C53 ◁ G | |
306 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 87 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53)(54,55);(56,57,58,63,59,64,67,75,60,65,68,76,69,77,80,85,61,62,66,72,70,73,78,82,71,74,79,83,81,84,86,87);(57,62)(58,66)(64,73)(65,74)(67,78)(68,79)(77,84)(80,86)4664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 6543);