Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10012 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#10035 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C22×C17 | #392 |
| prime radical | C17×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
498 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)(20,26)(21,29)(22,25)(23,28)(24,31)(27,33)(30,32)(34,35,39,43)(36,44,47,48)(37,42,38,41)(40,46,49,45);(23,32)(26,33)(34,36,39,47)(35,40,43,49)(37,46,38,45)(41,48,42,44);(18,20)(19,23)(21,30)(22,27)(24,33)(25,32)(26,29)(28,31)(36,45)(37,38)(40,44)(41,42)(46,47)(48,49)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3023);