Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9159 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#9168 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C2×#41×C17 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
432 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,26,23,27,21,25)(20,28,29,24,31,32,30,33)(34,35,40,43,38,37,39,42)(36,44,46,48,47,41,45,49);(18,20)(19,24)(21,29)(22,30)(23,31)(25,32)(26,28)(27,33)(34,36,39,46,38,47,40,45)(35,41,43,48,37,44,42,49);(18,21,23,22)(19,25,27,26)(20,29,31,30)(24,32,33,28)(34,37,38,35)(36,44,47,41)(39,42,40,43)(45,48,46,49)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2156);