Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C67 · Schur multiplier (H2) = C213 |
| direct product | C67×#62781 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C67 |
| socle | C22×C67 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ G | |
7230 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 6 generators on 91 points:
(1,2)(3,6)(4,5)(7,8)(9,10)(11,14)(12,19)(13,16)(15,20)(17,23)(18,22)(21,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(2,5)(6,8)(9,11,13,18)(10,14,16,22)(12,17,20,24)(15,21,19,23);(9,12)(10,15)(11,17)(13,20)(14,21)(16,19)(18,24)(22,23);(12,20)(15,19)(17,24)(21,23);(10,16)(14,22)(15,19)(21,23);(1,3,4,7)(2,6,5,8)5896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 55769);