Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C26 |
| direct product | C53×#24474 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| prime radical | C53×#3586 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C22×C4×C53 ◁ G | |
1298 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2,6,12,8,5,7,11)(3,13,17,15,18,28,16,9)(4,19,23,21,24,27,22,10)(14,25,20,26,31,30,32,29)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(1,3)(2,9)(4,20)(5,15)(6,17)(7,16)(8,18)(10,26)(11,28)(12,13)(14,22)(19,30)(21,29)(23,31)(24,32)(25,27);(1,4,8,24)(2,10,5,21)(3,14,18,31)(6,22,7,23)(9,25,15,30)(11,19,12,27)(13,29,28,26)(16,20,17,32);(1,5)(2,8)(3,15)(4,21)(6,11)(7,12)(9,18)(10,24)(13,16)(14,30)(17,28)(19,22)(20,29)(23,27)(25,31)(26,32)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 17462);