Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#33496 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C67 | C24 |
| commutator | C2 | C23×C16×C67 |
| Frattini, cosocle | C2×C8 | C24×C67 |
| socle | C22×C67 | C23×C8 |
| prime radical | C23×C67 | C22×C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C67 ◁ G | |
526 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(17,18,19,22,20,23,25,28,21,24,26,29,27,30,31,32)(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);(1,3,5,11)(2,6,8,9)(4,12,13,10)(7,15,16,14);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15);(2,8)(6,9)(7,16)(14,15)9112 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26484);