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×#10538 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C53 | #121 |
| commutator, Frattini, cosocle | C2×C42 | C23×C53 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C2×C42×C53 ◁ G | |
486 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 generators on 81 points:
(1,2)(3,4)(6,10)(7,8)(11,12)(13,14,19,24)(15,25,27,21)(16,28,26,20)(17,23,18,22)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81);(6,11)(7,8)(10,12)(13,15,19,27)(14,20,24,28)(16,18,26,17)(21,23,25,22);(2,4)(5,6)(7,11)(8,10)(9,12)(13,16,17,15,19,26,18,27)(14,21,22,20,24,25,23,28)2438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 3526);