Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #468 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C4 |
| direct product | C7×#491 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C7 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C42×C7 ◁ G | |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2)(3,5)(4,6)(7,8)(9,10,15,20)(11,21,23,17)(12,24,22,16)(13,19,14,18)(25,26,27,28,29,30,31);(1,3,4,7)(2,5,6,8)(9,11,13,22,15,23,14,12)(10,16,18,21,20,24,19,17);(2,6)(5,8)(9,12,13,11,15,22,14,23)(10,17,18,16,20,21,19,24)112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 899);