Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1714 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C53×#1722 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C53 | #127 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| prime radical | C2×#127×C53 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C2×C42×C53 ◁ G | |
914 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 79 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);(57,60)(58,61)(62,63)(64,65,68,71)(66,72,73,79)(67,75,76,70)(69,77,78,74);(64,66,67,74,68,73,76,77)(65,69,70,72,71,78,75,79);(56,57,61,63,59,62,58,60)(66,73)(69,78)(72,79)(74,77)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 12603);