Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9431 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#9434 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C23×C17 | #123 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
400 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)(19,23)(20,26)(21,29)(25,31)(27,28)(30,32)(34,35,40,43,38,37,39,42)(36,44,46,48,47,41,45,49);(18,19,21,23,22,25,29,31)(20,24,27,30,28,33,26,32)(34,36,39,46,38,47,40,45)(35,41,43,48,37,44,42,49);(18,20)(19,24)(21,27)(22,28)(23,30)(25,33)(26,29)(31,32)(34,37,38,35)(36,44,47,41)(39,42,40,43)(45,48,46,49)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2422);