Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C25×C4 |
| direct product | C67×#21244 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C67 | C2×#121 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| socle | C2×C67 | C2×#390 |
| prime radical | C2×#575×C67 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C67 ◁ C23×C4×C67 ◁ G | |
1460 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)(3,7,12,21)(4,14)(5,17)(6,9)(8,16)(10,18)(11,23,24,32)(13,27,26,20)(15,28)(19,30,31,25)(22,29)(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)(2,7,9,21)(4,11)(5,13)(6,12)(8,19,22,31)(10,20,17,27)(14,23,28,32)(15,24)(16,25)(18,26)(29,30);(1,4,5,16,6,15,18,29)(2,8,10,14,9,22,17,28)(3,11,13,25,12,24,26,30)(7,19,20,23,21,31,27,32);(4,15)(8,22)(11,24)(14,28)(16,29)(19,31)(23,32)(25,30)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 14232);