Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| isoclinism | isoclinic class of A4×D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2 |
| direct product | A4×Dic17 |
| unambiguous semidirect product | (C22×Dic17)⋊C3 |
| derived | C22×C17 ⋊ C3×C4 |
| Hall | C22×Dic17 ⋊ C3 |
| Sylow | C17 ⋊ C4×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4×D17 |
| commutator, hypocenter | C22×C17 | C3×C4 |
| Fitting, socle, cosocle | C23×C17 | C2×C3 |
| prime radical | C2×A4×C17 | C2 |
| LCS | G ▷ C22×C17 | |
| UCS | C1 ◁ C2 | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 204 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | A4⋊#3624, A4×#3624, #13109627, … |
| maximal normal subgroup of | A4⋊#3624, A4×#3624, #13109627, … |
| maximal quotient of | A4×#3622, SL(2,𝔽3)×Dic17, #10587634⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 106);