Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13310 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#13310 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | #1999 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C22×C4×C53 ◁ C2×#131×C53 ◁ G | |
552 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 points:
(1,2)(3,12)(4,7)(5,20)(6,11)(8,14)(9,17)(10,18)(13,25)(15,26)(16,27)(19,23)(21,29)(22,31)(24,28)(30,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(2,7)(4,17)(5,18)(8,24)(9,10)(11,23)(12,25)(13,28)(14,15)(19,31)(20,22)(21,26)(27,32)(29,30);(1,3)(2,8)(4,13)(5,15)(6,16)(7,21)(9,25)(10,27)(11,26)(12,20)(14,18)(17,28)(19,30)(22,32)(23,24)(29,31)1802 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 6298);