Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#9236 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #121 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C22×C17 | #386 |
| prime radical | C23×C17 | #120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
474 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
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)(18,19,22,25,23,26,21,31)(20,27,30,32,28,33,29,24)(34,35)(36,40,37,45)(38,43)(39,42)(41,46,49,44)(47,48);(18,20)(19,24,26,32)(21,29)(22,30)(23,28)(25,27,31,33)(34,36)(35,40,42,45)(37,39)(38,46)(41,43,49,48)(44,47);(20,28)(24,32)(27,33)(29,30)(34,37,39,36)(35,41,42,49)(38,44,47,46)(40,48,45,43)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2224);