Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#11258 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C67 | C2×D4 |
| commutator | C22×C4 | C22×C4×C67 |
| Frattini, cosocle | C23×C4 | C23×C67 |
| socle | C23×C67 | C4×D4 |
| prime radical | C24×C67 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C67 ◁ C23×C8×C67 ◁ G | |
654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 3 generators on 91 points:
(2,3)(5,6,8,7)(9,10,13,17,14,18,23,24)(11,15,19,21,20,12,16,22)(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);(1,2,4,3)(5,7,8,6)(9,11)(10,15)(12,18)(13,19)(14,20)(16,23)(17,21)(22,24);(1,3,4,2)(6,7)(9,12)(10,16)(11,17)(13,22)(14,15)(18,19)(20,24)(21,23)4288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 4246);