Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C23×C4 |
| direct product | C67×#22588 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | C22×D4 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| socle | C22×C67 | C2×C4×D4 |
| prime radical | C22×#41×C67 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C2×C22⋊C8×C67 ◁ G | |
888 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2)(3,5)(4,6)(7,8)(9,10,13,17,14,11,18,16)(12,15,23,24,21,19,22,20)(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);(1,3,4,7)(2,5,6,8)(9,11)(10,14)(12,20)(13,16)(15,23)(17,18)(19,22)(21,24);(2,6)(5,8)(12,21)(15,19)(20,24)(22,23);(9,12)(10,15)(11,19)(13,23)(14,21)(16,20)(17,24)(18,22)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 15576);