Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C23×C4 |
| direct product | C67×#20786 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C67 | C24 |
| commutator | C23 | C23×C4×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| socle | C23×C67 | C23×C4 |
| prime radical | C24×C67 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C67 ◁ G | |
758 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2)(3,6)(4,5)(7,8)(9,10)(11,13)(12,14)(15,16)(17,18,21,25,20,24,28,32)(19,22,27,29,26,23,30,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(2,5)(6,8)(9,11,12,15)(10,13,14,16)(17,19,20,26)(18,22,24,23)(21,27,28,30)(25,29,32,31);(10,14)(13,16)(17,19)(18,23)(20,26)(21,27)(22,24)(25,31)(28,30)(29,32);(1,3,4,7)(2,6,5,8)(19,26)(22,23)(27,30)(29,31)5092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 13774);