Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #1020 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#5936 |
| derived | C22⋊A4 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #1020 |
| commutator, hypocenter | C22⋊A4 | C3×C4 |
| Frattini | C2 | C3×#1020 |
| Fitting, socle | C25×C3 | D3 |
| prime radical | C2×C3×C22⋊A4 | C2 |
| cosocle | C2×C22⋊A4 | C2×C3 |
| LCS | G ▷ C22⋊A4 | |
| UCS | C1 ◁ C2×C3 | |
314 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #11920746, #11920748, #11920750, … |
| maximal normal subgroup of | #11920746, #11920748, #11920750, … |
| maximal quotient of | C3×#85561, C3×#85562, C3×#85563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8481);