Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C2×C4 |
| direct product | C67×#9792 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | #390 |
| commutator | C22×C4 | C22×C4×C67 |
| Frattini, cosocle | C2×C42 | C23×C67 |
| prime radical | C23×C67 | C4×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
358 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 3 generators on 99 points:
(1,2,4,6,5,9,12,8)(3,10,13,7,11,14,16,15)(17,18,21,24,20,23,25,31)(19,22,27,30,26,29,28,32)(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);(2,6,9,8)(3,11)(7,10,15,14)(13,16)(17,19,25,27,20,26,21,28)(18,22,24,32,23,29,31,30);(1,3,12,16,5,11,4,13)(2,7,6,14,9,15,8,10)(18,23)(19,26)(24,31)(27,28)2680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 2780);