Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C4 |
| direct product | C7×#498 |
| 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 | |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6)(3,7,8,5)(10,13)(11,15)(14,16)(17,18,19,20,21,22,23);(1,3,4,8)(2,5,6,7);(9,10,11,13,12,14,15,16)154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 906);