Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C53 · Schur multiplier (H2) = C26 |
| direct product | C2×C53×#1477 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C53 | C2×D4 |
| commutator | C4 | C23×C8×C53 |
| Frattini, cosocle | C42 | C24×C53 |
| socle | C23×C53 | C2×C22⋊C4 |
| prime radical | C22×#41×C53 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C53 ◁ C22×C42×C53 ◁ G | |
1370 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 6784 |
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);(3,4,5,7,6,8,9,10)(12,15)(13,17)(16,18);(11,12)(13,18)(14,16)(15,17);(12,16)(15,18)4664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 10424);