Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C22 |
| direct product | C67×#8881 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | #120 |
| commutator | C22×C4 | C22×C4×C67 |
| Frattini, cosocle | C2×C42 | C23×C67 |
| socle | C22×C67 | #385 |
| prime radical | C23×C67 | C4×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C2×C42×C67 ◁ G | |
364 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 3 generators on 91 points:
(2,6)(3,7)(4,8)(9,10,14,17,15,18,13,20)(11,19,21,12,22,23,16,24)(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);(1,2,5,3)(4,7,8,6)(9,11,13,16,15,22,14,21)(10,12,20,19,18,24,17,23);(1,3,5,2)(4,6,8,7)(9,12,15,24)(10,16,18,21)(11,20,22,17)(13,19,14,23)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 1869);