Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18132 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#18156 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
982 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 2144 |
A minimal faithful permutation representation — 4 generators on 99 points:
(2,8)(4,17)(5,13)(9,25)(10,27)(11,24)(12,19)(14,31)(20,30)(22,23)(26,28)(29,32)(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);(1,2)(3,9)(4,10)(5,19)(6,12)(7,11)(8,13)(14,28)(15,26)(16,23)(17,22)(18,27)(20,32)(21,29)(24,30)(25,31);(1,3,6,15)(2,9,12,26)(4,13,17,5)(7,16,21,18)(8,22,19,10)(11,23,29,27)(14,30,31,20)(24,25,32,28);(1,4,7,14)(2,10,11,28)(3,13,16,30)(5,18,20,15)(6,17,21,31)(8,23,24,9)(12,22,29,25)(19,27,32,26)2479 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 11144);