Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3⋊#994 |
| unambiguous semidirect product | (C2×C3)⋊#994 |
| unambiguous semidirect product | (C2×#1009)⋊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 | |
429 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 429 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) = 144 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | #11920721, #11920722, #11920723, … |
| maximal normal subgroup of | #11920721, #11920722, #11920723, … |
| maximal quotient of | C2×SL(2,𝔽3)×Dic6, C2×#5574⋊C3, #85821⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8500);