Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#18092 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | C22×D4 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C42 | C24×C67 |
| socle | C22×C67 | C2×C4×D4 |
| prime radical | #466×C67 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ #431×C67 ◁ G | |
598 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)(3,12)(4,10)(5,9)(6,11)(7,13)(8,14)(15,16)(17,18,22,25,23,19,21,26)(20,27,29,32,30,24,28,31)(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);(1,3)(2,7)(4,13)(5,15)(6,14)(8,10)(9,12)(11,16)(17,19)(18,23)(20,27)(21,25)(22,26)(24,30)(28,31)(29,32);(1,3)(2,8)(4,15)(5,13)(6,14)(7,10)(9,16)(11,12)(17,20,22,29,23,30,21,28)(18,24,25,31,19,27,26,32);(1,4,6,5)(2,9,11,10)(3,13,14,15)(7,12,16,8)(17,21,23,22)(18,25,19,26)(20,28,30,29)(24,31,27,32)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 11080);