Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#396 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C23 |
| commutator, Frattini, cosocle | C23 | C23×C7 |
| prime radical | C24×C7 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
186 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)(10,11)(13,14,15,16,17,18,19);(5,6)(7,8)(9,10,12,11);(2,4)(6,8)(9,11)(10,12)154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 804);