Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#22685 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C67 | C22×D4 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ C4×C4⋊C4×C67 ◁ G | |
910 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 17152 |
A minimal faithful permutation representation — 4 generators on 91 points:
(2,4)(5,6,7,8)(10,15)(12,21)(13,19)(16,24)(17,22)(18,23)(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);(9,10,14,18)(11,16,20,17)(12,22,21,24)(13,23,19,15);(1,2,3,4)(9,11,14,20)(10,16,18,17)(12,19,21,13)(15,24,23,22);(9,12,14,21)(10,17,18,16)(11,19,20,13)(15,24,23,22)4690 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 15673);