Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10260 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#10587 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C53 | #121 |
| commutator, Frattini, cosocle | C2×C42 | C23×C53 |
| prime radical | C2×#127×C53 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C2×C42×C53 ◁ G | |
454 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 73 points:
(5,6,7,10,8,11,12,9)(14,19)(15,20)(16,17)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73);(1,2)(3,4)(13,14,16,19,18,20,17,15);(2,4)(6,9)(7,12)(10,11)(13,15)(14,17)(16,20)(18,19)2438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 3575);