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×#33560 |
| 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 ◁ C2×C4×C17 ◁ C2×#41×C17 ◁ G | |
1132 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)(24,30)(29,42)(31,43)(32,46)(33,39)(34,40)(35,41)(36,44)(37,45)(38,47)(48,49);(18,20,23,31)(19,24,27,37)(21,32,33,29)(22,30,35,45)(25,38,39,36)(26,28,41,43)(34,47,48,44)(40,46,49,42);(21,33)(22,35)(25,39)(29,32)(30,45)(36,38)(40,49)(42,46);(18,21,23,33)(19,25,27,39)(20,29,31,32)(22,34,35,48)(24,36,37,38)(26,40,41,49)(28,42,43,46)(30,44,45,47)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26548);