Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#18826 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C67 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
1114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2)(3,7)(4,6)(5,8)(10,15)(11,19)(12,13)(17,18)(20,21)(22,23)(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);(2,6)(3,4)(7,8)(9,10,14,18)(11,16,20,24)(12,15,13,17)(19,22,21,23);(9,11)(10,16)(12,19)(13,21)(14,20)(15,22)(17,23)(18,24);(1,3,5,4)(2,7,8,6)(9,12,14,13)(10,17,18,15)(11,19,20,21)(16,23,24,22)2479 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 11814);