Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24295 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C26 |
| direct product | C67×#24295 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | #2408 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C22×C4×C67 ◁ G | |
1302 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)(3,5)(4,17)(6,25)(7,12)(8,13)(9,15)(10,21)(11,23)(14,26)(16,24)(18,19)(20,28)(22,27)(29,32)(30,31)(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);(1,3,6,15,8,16,7,11)(2,9,12,5,13,23,25,24)(4,18,20,14,22,29,21,30)(10,19,27,31,28,32,17,26);(1,4)(2,10)(3,14)(5,19)(6,20)(7,21)(8,22)(9,26)(11,18)(12,27)(13,28)(15,29)(16,30)(17,25)(23,31)(24,32);(1,5,6,23,8,24,7,9)(2,11,12,3,13,15,25,16)(4,19,20,31,22,32,21,26)(10,18,27,14,28,29,17,30)2680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 17283);