Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C28 |
| direct product | C67×#61620 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ #525×C67 ◁ G | |
2088 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 5 generators on 91 points:
(1,2)(3,7)(4,6)(5,8)(9,10,15,11)(12,20,22,24)(13,17,14,19)(16,23,18,21)(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);(1,3)(2,5)(4,8)(6,7)(9,11,15,10)(12,18,22,16)(13,17,14,19)(20,21,24,23);(9,12)(10,16)(11,18)(13,21)(14,23)(15,22)(17,24)(19,20);(3,8)(5,7);(2,6)(5,7)(9,13,15,14)(10,17,11,19)(12,21,22,23)(16,24,18,20)3283 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54608);