Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21782 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#21784 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2308 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
1278 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28,31,24)(21,32,34,44)(22,27)(23,26)(25,33,41,36)(29,45)(30,43,35,39)(37,42)(38,46)(40,48)(47,49);(18,20)(19,24)(21,29)(22,35)(23,31)(25,40)(26,28)(27,43)(30,37)(32,49)(33,48)(34,47)(36,46)(38,41)(39,42)(44,45);(18,21,23,34)(19,25,26,41)(20,29,31,47)(22,36,37,33)(24,38,28,40)(27,44,42,32)(30,48,35,46)(39,45,43,49);(18,20)(19,24)(21,29)(22,30)(23,31)(25,38)(26,28)(27,39)(32,49)(33,46)(34,47)(35,37)(36,48)(40,41)(42,43)(44,45)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14772);