Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24412 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C24×C4 |
| direct product | C67×#25921 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C22×D4×C67 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
972 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2,5,8)(3,7,4,6)(9,10)(11,16)(12,19)(13,17)(14,23)(15,18)(20,21)(22,24)(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);(1,3,5,4)(2,6,8,7)(9,11)(10,16)(12,17)(13,19)(14,24)(15,20)(18,21)(22,23);(1,3,5,4)(2,7,8,6)(9,12,14,16,15,22,13,21)(10,11,17,19,18,20,23,24);(1,4,5,3)(2,7,8,6)(9,13,15,14)(10,17,18,23)(11,19,20,24)(12,21,22,16)2881 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 18909);