Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | C22×#41⋊C9 |
| Sylow | C22×#41 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C4 | A4 |
| commutator, hypocenter | Q8 | C23×C9 |
| Frattini | C2×C3 | C23×A4 |
| Fitting, prime radical | C22×C3×#41 | C3 |
| socle | C23×C3 | C2×A4 |
| cosocle | C3×Q8 | C23×C3 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C22×C3×C4 | |
397 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #2341⋊C9, #2880⋊C9, C2×C4×#41⋊C9, … |
| maximal normal subgroup of | #2341⋊C9, #2880⋊C9, C2×C4×#41⋊C9, … |
| maximal quotient of | C22×C4×Q8⋊C9, C2×C4×#41⋊C9, C2×#548⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4998);