Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10518 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C67 · Schur multiplier (H2) = C22 |
| direct product | C67×#10521 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C67 |
| prime radical | #532×C67 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
420 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 3 generators on 91 points:
(1,2,6,8)(3,5,7,4)(9,10,14,18)(11,12,16,22)(13,19,24,17)(15,23,21,20)(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);(2,3)(4,5)(7,8)(9,11)(10,15)(12,19)(13,23)(14,16)(17,22)(18,21)(20,24);(1,3,5,8,6,7,4,2)(9,12,13,21,14,22,24,15)(10,16,17,23,18,11,19,20)2680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 3509);