Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9431 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C23 |
| direct product | C67×#9432 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | #386 |
| commutator | C42 | C22×C4×C67 |
| Frattini, cosocle | C2×C42 | C23×C67 |
| prime radical | C67×#3180 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
436 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 3 generators on 99 points:
(2,6)(3,10)(4,7)(9,14)(11,12)(13,15)(17,18)(19,26,27,30)(20,23,28,29)(21,24)(22,25)(31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,2,7,14,5,9,4,6)(3,8,10,15,12,16,11,13)(17,19,21,29,22,27,31,23)(18,20,24,30,25,28,32,26);(1,3)(2,8)(4,11)(5,12)(6,13)(7,10)(9,16)(14,15)(17,20)(18,23)(19,24)(21,30)(22,28)(25,29)(26,31)(27,32)2680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 2420);