Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C67 · Schur multiplier (H2) = C213 |
| direct product | C67×#62752 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C67 |
| socle | C22×C67 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ G | |
6528 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 6 generators on 99 points:
(1,2)(3,9)(4,8)(5,7)(6,10)(11,15)(12,14)(13,16)(17,18)(19,22)(20,24)(21,23)(25,30)(26,29)(27,32)(28,31)(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)(2,6)(4,11)(5,10)(7,9)(8,13)(12,16)(14,15)(17,19,21,26)(18,22,23,29)(20,27,28,25)(24,32,31,30);(3,10)(6,9)(11,16)(13,15)(18,23)(22,29)(24,31)(30,32);(2,7)(6,9)(8,14)(13,15)(17,20,21,28)(18,24,23,31)(19,25,26,27)(22,30,29,32);(18,23)(22,29)(24,31)(30,32);(1,4,5,12)(2,8,7,14)(3,11,10,16)(6,13,9,15)5092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 55740);