Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8×C67 · Schur multiplier (H2) = C24×C4 |
| direct product | C67×#20569 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C67 | C24 |
| commutator | C2 | C22×C4×C8×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| socle, prime radical | C23×C67 | C23×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C67 ◁ G | |
990 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 17152 |
A minimal faithful permutation representation — 4 generators on 87 points:
(5,6)(7,10)(8,11)(9,12)(13,14,16,19,17,15,18,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(1,2,3,4)(5,7,10,6)(8,11,9,12);(5,8,10,9)(6,11,7,12)(13,15,16,20,17,14,18,19);(5,9,10,8)(6,11,7,12)9112 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 13557);