Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12753 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#12757 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | #1790 |
| commutator | C2×D4 | C22×C4×C67 |
| Frattini, cosocle | C2×#41 | C23×C67 |
| prime radical | #525×C67 | C22 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C2×C4×C67 ◁ C2×#41×C67 ◁ G | |
736 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 2144 |
A minimal faithful permutation representation — 3 generators on 99 points:
(1,2,5,9,6,10,19,26)(3,11,14,28,13,27,31,32)(4,15,17,25,16,8,18,23)(7,20,21,12,22,29,24,30)(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);(1,3,6,13)(2,7,10,22)(4,12,16,30)(5,14,19,31)(8,11,15,27)(9,24,26,21)(17,29,18,20)(23,32,25,28);(8,15)(11,27)(23,25)(28,32)2278 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 5745);