Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33657 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#33659 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | C2×#481 |
| commutator, Frattini, cosocle | C2×C8 | C24×C67 |
| prime radical | C67×#3060 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C22×C4×C67 ◁ C2×#131×C67 ◁ G | |
546 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)(3,12)(4,9)(5,18)(6,16)(7,11)(8,15)(10,21)(13,27)(14,29)(17,19)(20,26)(22,32)(23,30)(24,31)(25,28)(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)(3,8)(4,16)(5,19)(6,9)(7,11)(10,22)(12,28)(13,26)(14,25)(15,29)(17,18)(20,30)(21,32)(23,24)(27,31);(1,3,6,23,7,14,4,13)(2,8,9,24,11,25,16,26)(5,20,21,28,22,31,17,15)(10,27,18,29,19,30,32,12);(1,4,7,6)(2,9,11,16)(3,13,14,23)(5,17,22,21)(8,24,25,26)(10,18,19,32)(12,27,29,30)(15,31,28,20)2680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26647);