Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17411 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C24×C4 |
| direct product | C67×#22478 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C67 |
| Frattini, cosocle | C24 | C24×C67 |
| prime radical | C22×D4×C67 | C23 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C22×C4⋊C4×C67 ◁ G | |
1132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 91 points:
(2,5)(6,8)(9,10)(11,15)(12,20,22,16)(13,17)(14,18)(19,24,21,23)(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);(1,2)(3,6)(4,5)(7,8)(9,11,14,13)(10,15,18,17)(12,19,22,21)(16,23,20,24);(1,3,4,7)(2,6,5,8)(9,12)(10,16)(11,19)(13,21)(14,22)(15,23)(17,24)(18,20);(2,5)(6,8)(9,13,14,11)(10,17,18,15)(12,21,22,19)(16,24,20,23)3685 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 15466);