Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#17957 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C67 | C2×D4 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C42 | C24×C67 |
| socle | C22×C67 | C2×C4×D4 |
| prime radical | #532×C67 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C67 ◁ C2×C4×C8×C67 ◁ G | |
682 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 91 points:
(2,5)(3,7)(6,8)(9,10,14,17,15,11,13,19)(12,16,21,23,22,18,20,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,2,4,6)(3,8,7,5)(9,11,15,10)(12,18,22,16)(13,17,14,19)(20,23,21,24);(9,12,14,21,15,22,13,20)(10,16,17,23,11,18,19,24);(10,11)(16,18)(17,19)(23,24)5896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 10945);