Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C3×C4×C3⋊C8 |
| derived | C3 ⋊ C2×C3×C4×C8 |
| Sylow | C32 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C42 | D3 |
| commutator, hypocenter | C3 | C2×C3×C4×C8 |
| Frattini | C2×C4 | C22×C3×D3 |
| Fitting | C2×C32×C42 | C2 |
| socle, prime radical | C23×C32 | C2×C4 |
| cosocle | C2×C3×C4 | C23×C3 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C3×C42 | |
378 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 270 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C3⋊#1273, #11770700, C3×#67703, … |
| maximal normal subgroup of | C3×C3⋊#1273, #11770700, C3×#67703, … |
| maximal quotient of | C2×C3×C8×C3⋊C8, C2×C3×#4455, C3×M16×C3⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3899);