Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#22692 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | D42 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C2×#135×C67 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C22×C4×C67 ◁ G | |
862 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 87 points:
(1,2,3,4)(6,11)(7,16)(9,17)(13,18)(14,15)(19,20)(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);(5,6,10,15)(7,12,18,8)(9,14,17,11)(13,20,16,19);(5,7,17,13,10,18,9,16)(6,12,11,20,15,8,14,19);(5,8)(6,13)(7,14)(9,20)(10,12)(11,18)(15,16)(17,19)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 15680);