Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#21184 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C67 | C2×#121 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| socle | C2×C67 | C2×#389 |
| prime radical | C24×C67 | C2×Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C67 ◁ C23×C4×C67 ◁ G | |
844 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 2144 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2,6,10,7,11,5,21)(3,12,14,8,16,23,15,24)(4,17,20,25,18,31,19,9)(13,22,28,30,27,32,29,26)(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);(1,3,6,14,7,16,5,15)(2,8,10,23,11,24,21,12)(4,13,20,28,18,27,19,29)(9,22,17,30,25,32,31,26);(1,4,5,19,7,18,6,20)(2,9,10,17,11,25,21,31)(3,13,15,29,16,27,14,28)(8,22,23,30,24,32,12,26);(4,18)(9,25)(13,27)(17,31)(19,20)(22,32)(26,30)(28,29)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 14172);