Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61109 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C29 |
| direct product | C53×#61111 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | C2×D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C53 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C22×C4×C53 ◁ G | |
2600 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 5 generators on 85 points:
(2,8)(3,13)(5,21)(6,23)(9,24)(10,15)(11,12)(14,28)(16,26)(17,31)(18,19)(25,30)(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);(1,2)(3,5)(4,16)(6,11)(7,12)(8,23)(9,18)(10,21)(13,22)(14,29)(15,27)(17,28)(19,26)(20,24)(25,32)(30,31);(1,3,7,10)(2,5,12,21)(4,14,20,25)(6,15,23,13)(8,22,11,27)(9,17,26,31)(16,29,24,32)(18,28,19,30);(1,4)(2,9)(3,14)(5,17)(6,19)(7,20)(8,24)(10,25)(11,16)(12,26)(13,28)(15,30)(18,23)(21,31)(22,32)(27,29);(1,5)(2,10)(3,12)(4,17)(6,22)(7,21)(8,13)(9,25)(11,15)(14,26)(16,30)(18,29)(19,32)(20,31)(23,27)(24,28)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 54099);