Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33557 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#33558 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C17 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C23×C17 ◁ C22×D4×C17 ◁ G | |
1158 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)(21,25)(22,26)(23,27)(24,31)(29,41)(30,42)(32,38)(33,39)(34,47)(35,40)(36,43)(37,45)(44,49)(46,48);(18,20,23,30)(19,24,27,37)(21,29,32,44)(22,31,35,45)(25,36,38,48)(26,28,40,42)(33,43,34,46)(39,41,47,49);(18,21)(19,25)(20,29)(22,34)(23,32)(24,36)(26,39)(27,38)(28,41)(30,44)(31,46)(33,35)(37,48)(40,47)(42,49)(43,45);(20,30)(21,32)(24,37)(25,38)(28,42)(31,45)(33,34)(39,47)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26546);