Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9519 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C23 |
| direct product | C67×#9532 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | #386 |
| commutator | C22×C4 | C22×C4×C67 |
| Frattini, cosocle | C2×C42 | C23×C67 |
| prime radical | #447×C67 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
444 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 3 generators on 99 points:
(1,2,4,7,6,10,5,9)(3,11,12,8,13,15,14,16)(17,18,23,26)(19,22,25,21)(20,27)(24,28)(29,31)(30,32)(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);(2,7,10,9)(8,15,16,11)(17,19,21,18,23,25,22,26)(20,27,29,24,30,32,28,31);(1,3)(2,8)(4,12)(5,14)(6,13)(7,15)(9,11)(10,16)(17,20)(18,24)(19,27)(21,29)(22,28)(23,30)(25,32)(26,31)2479 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 2520);