Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C28 |
| direct product | C67×#61667 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ #532×C67 ◁ G | |
2064 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 5 generators on 91 points:
(1,2)(3,7)(4,6)(5,8)(10,16)(11,19)(13,15)(17,24)(20,23)(21,22)(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);(1,3)(2,5)(4,8)(6,7)(9,10,14,16)(11,17,21,23)(12,15,18,13)(19,20,22,24);(9,11)(10,17)(12,20)(13,19)(14,21)(15,22)(16,23)(18,24);(3,8)(5,7)(9,12,14,18)(10,13,16,15)(11,20,21,24)(17,19,23,22);(2,6)(5,7)(9,13,14,15)(10,18,16,12)(11,19,21,22)(17,24,23,20)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54655);