Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23892 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C27 |
| direct product | C53×#23894 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C22×C4×C53 ◁ G | |
1642 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2,7,12)(3,13,18,28)(4,19,21,26)(5,11,6,10)(8,17,25,16)(9,22,27,20)(14,23,32,30)(15,24,31,29)(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)(2,8)(4,15)(5,17)(6,16)(7,18)(9,24)(10,28)(11,13)(12,25)(14,20)(19,30)(21,31)(22,32)(23,26)(27,29);(1,4)(2,9)(3,14)(5,20)(6,22)(7,21)(8,23)(10,19)(11,26)(12,27)(13,29)(15,16)(17,31)(18,32)(24,28)(25,30);(1,4)(2,9)(3,15)(5,22)(6,20)(7,21)(8,24)(10,26)(11,19)(12,27)(13,30)(14,16)(17,32)(18,31)(23,28)(25,29)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 16882);