Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #7092 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C67 · Schur multiplier (H2) = C22 |
| direct product | C67×#7096 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | #331 |
| commutator | C4×C8 | C2×C4×C67 |
| Frattini, cosocle | C82 | C22×C67 |
| prime radical | C67×#1712 | C2 |
| LCS | G ▷ C4×C8 ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C42×C67 ◁ C82×C67 ◁ G | |
186 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 2 generators on 99 points:
(1,2,3,8,4,7,11,15,5,9,12,16,13,6,10,14)(17,18)(19,22)(20,29)(21,25)(23,26)(24,27)(28,31)(30,32)(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);(2,6)(3,10)(4,13)(7,9)(8,16)(11,12)(18,22)(19,26)(20,27)(23,24)(25,31)(28,32)(29,30)2881 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 84);