Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10046 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#10061 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C53 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C53 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C2×C42×C53 ◁ G | |
534 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 generators on 89 points:
(5,6,10,13)(7,14,16,19)(8,12,9,17)(11,18,20,15)(21,22,26,30)(23,31,34,35)(24,27,25,29)(28,32,36,33)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(1,2)(3,4)(5,7,10,16)(6,11,13,20)(8,15,9,18)(12,19,17,14)(22,27)(24,25)(28,35)(29,30)(31,36)(32,33);(2,4)(5,8,10,9)(6,12,13,17)(7,15,16,18)(11,19,20,14)(21,23,26,34)(22,28,30,36)(24,33,25,32)(27,35,29,31)2438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 3049);