Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×GU(3,𝔽2) |
| Fitting | C2×H(3,𝔽3) ⋊ SL(2,𝔽3) |
| derived | SU(3,𝔽2) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C3 | PSU(3,𝔽2)⋊C3 |
| commutator, cosocle, hypocenter | SU(3,𝔽2) | C2×C3 |
| Frattini | C3 | C2×PSU(3,𝔽2)⋊C3 |
| Fitting | C2×H(3,𝔽3) | SL(2,𝔽3) |
| LCS | G ▷ SU(3,𝔽2) | |
| UCS | C1 ◁ C2×C3 | |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | Sp(4,𝔽3), #72214508, C2×#72209952, … |
| maximal normal subgroup of | C2×GU(3,𝔽2)⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2895);