Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7606 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C23 |
| direct product | C67×#7620 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C67 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C67 |
| Frattini, cosocle | C2×C42 | C23×C67 |
| prime radical | C2×#121×C67 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ C22×C42×C67 ◁ G | |
590 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 3 generators on 91 points:
(1,2)(3,7,8,5)(4,6)(10,14,15,16)(17,18,20,22,21,23,19,24)(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);(1,3)(2,5)(4,8)(6,7)(9,10)(11,14)(12,16)(13,15)(18,22)(19,20)(23,24);(9,11,13,12)(10,14,15,16)(18,23)(22,24)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 608);