Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#23622 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C67 | #396 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| socle | C2×C67 | C2×#396 |
| prime radical | C22×#41×C67 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C67 ◁ C23×C4×C67 ◁ G | |
960 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 2144 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2,7,11,6,12,5,10)(3,13,21,24,16,23,15,8)(4,9,18,25,20,26,19,27)(14,28,29,22,17,31,30,32)(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);(1,3,5,15,6,16,7,21)(2,8,11,13,12,24,10,23)(4,17,19,29,20,14,18,30)(9,22,25,31,26,32,27,28);(1,4)(2,9)(3,14)(5,18)(6,20)(7,19)(8,22)(10,25)(11,27)(12,26)(13,28)(15,29)(16,17)(21,30)(23,31)(24,32);(1,5,6,7)(2,10,12,11)(3,15,16,21)(4,18,20,19)(8,23,24,13)(9,25,26,27)(14,29,17,30)(22,31,32,28)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 16610);