Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C26 |
| direct product | C53×#24410 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C22×C4×C53 ◁ G | |
1322 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)(3,7,13,21)(4,8,15,23)(5,10)(6,9)(11,14,22,18)(12,20)(16,24,28,30)(17,19)(25,29)(26,32)(27,31)(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);(1,3,5,13)(2,7,10,21)(4,12,15,26)(6,18,17,14)(8,20,23,32)(9,11,19,22)(16,29,28,27)(24,25,30,31);(1,2)(3,11)(4,8)(5,10)(6,19)(7,18)(9,17)(12,25)(13,22)(14,21)(15,23)(16,30)(20,29)(24,28)(26,31)(27,32);(1,4)(2,8)(3,12)(5,15)(6,16)(7,20)(9,24)(10,23)(11,25)(13,26)(14,27)(17,28)(18,29)(19,30)(21,32)(22,31)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 17398);