Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1828 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C53 · Schur multiplier (H2) = C26 |
| direct product | C2×C53×#1830 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #381 |
| commutator | C23 | C23×C4×C53 |
| Frattini, cosocle | C22×C4 | C24×C53 |
| prime radical | C24×C53 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C23×C4×C53 ◁ G | |
1218 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 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);(56,57,60,65,61,64,74,79)(58,66,68,80,69,62,73,76)(59,70,72,84,71,63,77,78)(67,75,83,86,82,81,85,87);(56,58,61,69)(57,62,64,66)(59,67,71,82)(60,73,74,68)(63,75,70,81)(65,80,79,76)(72,85,77,83)(78,87,84,86);(56,59)(57,63,64,70)(58,67)(60,72)(61,71)(62,75,66,81)(65,78,79,84)(68,83)(69,82)(73,85)(74,77)(76,86,80,87)3074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 13700);