Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18316 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#18327 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C24×C67 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C23×C4×C67 ◁ G | |
950 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2,5,7)(3,9,11,16)(4,12,14,8)(6,13,15,10)(17,18)(19,22)(20,23)(21,24)(25,31)(26,29)(27,30)(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);(1,3,5,11)(2,6,7,15)(4,13,14,10)(8,16,12,9)(17,19)(18,22)(20,25)(21,26)(23,28)(24,29)(27,32)(30,31);(17,20,21,27)(18,23,24,30)(19,25,26,32)(22,28,29,31);(2,7)(6,15)(8,12)(9,16)(18,24)(22,29)(23,30)(28,31)2479 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 11315);