Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C67 · Schur multiplier (H2) = C23×C4 |
| direct product | C67×#10916 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | #386 |
| commutator | C23 | C2×C42×C67 |
| Frattini, cosocle | C23×C4 | C23×C67 |
| prime radical | C24×C67 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C23×C4×C67 ◁ G | |
718 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 3 generators on 87 points:
(1,2,4,3)(6,10)(8,15)(14,19)(18,20)(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);(5,6,8,12,9,10,15,17)(7,11,14,18,13,16,19,20);(1,3,4,2)(5,7)(6,11)(8,14)(9,13)(10,16)(12,18)(15,19)(17,20)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 3904);