Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C28 |
| direct product | C67×#61608 |
| 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 ◁ C2×C4×D4×C67 ◁ G | |
2132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 5 generators on 91 points:
(1,2)(3,7)(4,6)(5,8)(9,10,13,15)(11,19,21,24)(12,17,14,18)(16,22,23,20)(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)(10,15)(16,23)(17,18)(19,24);(9,11)(10,16)(12,20)(13,21)(14,22)(15,23)(17,24)(18,19);(3,8)(5,7)(9,12,13,14)(10,17,15,18)(11,20,21,22)(16,24,23,19);(2,6)(5,7)(9,12,13,14)(10,18,15,17)(11,20,21,22)(16,19,23,24)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54596);