Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C24×C4 |
| direct product | C67×#21088 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C67 | C22×D4 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C24×C67 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ C2×#117×C67 ◁ G | |
1074 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2)(3,4)(5,6,8,7)(9,10)(11,20)(12,21)(13,18)(14,24)(15,19)(16,17)(22,23)(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);(5,7,8,6)(9,11,14,17,15,21,13,23)(10,16,18,20,19,22,24,12);(2,4)(9,12,14,16,15,20,13,22)(10,17,18,21,19,23,24,11);(9,13,15,14)(10,18,19,24)(11,17,21,23)(12,22,20,16)4288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 14076);