Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23882 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C27 |
| direct product | C67×#23883 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C22×C4×C67 ◁ G | |
1696 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)(3,13)(4,17)(5,10)(6,11)(7,12)(8,15)(9,19)(14,22)(16,27)(18,26)(20,25)(21,23)(24,30)(28,29)(31,32)(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)(2,8)(4,14)(5,21)(6,15)(7,16)(9,24)(10,13)(11,27)(12,23)(17,28)(18,31)(19,29)(20,30)(22,26)(25,32);(1,4,7,20)(2,9,12,26)(3,14,16,30)(5,19,6,18)(8,22,23,24)(10,25,11,17)(13,28,27,32)(15,31,21,29);(2,10)(5,6)(8,13)(9,25)(11,12)(15,21)(17,26)(18,19)(22,28)(23,27)(24,32)(29,31)2680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 16871);