Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#17920 |
| 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 | C67×#3106 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ #431×C67 ◁ G | |
638 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)(3,8)(4,9)(5,14)(6,10)(7,11)(12,15)(13,16)(17,18,20,24,21,23,27,30)(19,22,25,29,26,28,31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,3)(2,7)(4,11)(5,13)(6,12)(8,14)(9,15)(10,16);(1,3)(2,8)(4,13)(5,11)(6,12)(7,14)(9,16)(10,15)(17,19,20,25,21,26,27,31)(18,22,24,29,23,28,30,32);(1,4,6,5)(2,9,10,14)(3,11,12,13)(7,15,16,8)(18,23)(22,28)(24,30)(29,32)4288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 10908);