Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C67 · Schur multiplier (H2) = C25×C4 |
| direct product | C67×#20398 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C22×C22⋊C4 |
| commutator | C22 | C22×C42×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C23×D4×C67 | C22 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×#117×C67 ◁ G | |
1658 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 2144 |
A minimal faithful permutation representation — 4 generators on 87 points:
(1,2,4,3)(5,6)(7,14)(8,12)(9,18)(10,13)(11,16)(15,20)(17,19)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(5,7,9,17,10,16,8,15)(6,11,12,19,13,14,18,20);(1,3,4,2)(5,6)(7,11)(8,18)(9,12)(10,13)(14,16)(15,20)(17,19);(5,8,10,9)(6,12,13,18)(7,15,16,17)(11,19,14,20)5494 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 13386);