Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#436 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C23 |
| commutator | C22 | C22×C4×C7 |
| Frattini, cosocle | C2×C4 | C23×C7 |
| socle | C22×C7 | C22×C4 |
| prime radical | C2×C7×D4 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ G | |
122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2)(3,4)(5,6,9,11,8,10,12,7)(13,14,15,16,17,18,19);(2,4)(6,10)(7,11);(5,7,9,6,8,11,12,10)196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 844);