Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #365 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#7180 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #106 |
| commutator | C8 | C4×C8×C17 |
| Frattini, cosocle | C2×C4×C8 | C22×C17 |
| socle | C2×C17 | #1279 |
| prime radical | C23×C17 | #104 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C22×C8×C17 ◁ C2×C4×C8×C17 ◁ G | |
240 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 2 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,28,24,30,40,45,25,31,39,27,23,29,21,38)(20,32,34,43,36,48,33,44,37,46,41,42,35,47,49,26);(18,20)(19,26,29,42,31,44,30,43)(21,33)(22,41)(23,35)(24,36)(25,37)(27,32,45,47,28,46,38,48)(34,39)(40,49)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 168);