Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C2×C7×#100 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22⋊C4 |
| commutator | C22 | C22×C4×C7 |
| Frattini, cosocle | C2×C4 | C23×C7 |
| prime radical | C22×C7×D4 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
186 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2)(3,4,5,6,7,8,9);(10,11,12,15,13,14,16,17);(11,14)(12,16)154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 819);