Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#11103 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C67 | #390 |
| commutator | C22×C4 | C22×C4×C67 |
| Frattini, cosocle | C23×C4 | C23×C67 |
| socle | C2×C67 | #1439 |
| prime radical | C22×#41×C67 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C67 ◁ C23×C4×C67 ◁ G | |
836 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 2144 |
A minimal faithful permutation representation — 3 generators on 99 points:
(1,2,6,10,7,11,5,20)(3,12,16,23,15,28,14,8)(4,17,18,25,19,9,21,26)(13,27,29,22,30,32,31,24)(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);(1,3,5,14,7,15,6,16)(2,8,10,12,11,23,20,28)(4,13,18,29,19,30,21,31)(9,24,25,32,17,22,26,27);(1,4)(2,9)(3,13)(5,18)(6,21)(7,19)(8,22)(10,25)(11,17)(12,27)(14,29)(15,30)(16,31)(20,26)(23,24)(28,32)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 4091);