Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×Ω+(4,𝔽3) |
| unambiguous semidirect product | (C2×SL(2,𝔽3))⋊A4 |
| unambiguous semidirect product | (C2×#994)⋊C3 |
| unambiguous semidirect product | (C2×#997)⋊C3 |
| Fitting, Sylow | C2×H(5,𝔽2) ⋊ C32 |
| derived | H(5,𝔽2) ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C22 | A42 |
| commutator, cosocle, hypocenter | H(5,𝔽2) | C2×C32 |
| Frattini | C2 | C2×A42 |
| Fitting | C2×H(5,𝔽2) | C32 |
| LCS | G ▷ H(5,𝔽2) | |
| UCS | C1 ◁ C22 | |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
50 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8359);