Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#1010⋊C3 |
| unambiguous semidirect product | (C2×#1010)⋊C3 |
| Fitting | C2×C3×#41 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D3×A4 |
| commutator, cosocle, hypocenter | C3×Q8 | C23×C3 |
| Frattini | C2 | C22×D3×A4 |
| Fitting | C2×C3×#41 | C2×C3 |
| socle | C22×C3 | C22×A4 |
| hypercenter | C2×C4 | D3×A4 |
| LCS | G ▷ C3×Q8 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
421 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 421 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | #11920718, #11920719, #11920720, … |
| maximal normal subgroup of | #11920718, #11920719, #11920720, … |
| maximal quotient of | C2×#5570⋊C3, C2×SL(2,𝔽3)×D12, C2×#5572⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8502);