Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#63958 |
| Sylow | C32 ⋊ C2×#121 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D32 |
| commutator, cosocle | C22×C32 | C24 |
| Frattini | C22 | C22×D32 |
| Fitting | C24×C32 | C22 |
| socle | C23×C32 | C23 |
| hypercenter | C24 | D32 |
| hypocenter | C32 | C2×#121 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C24 | |
970 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 970 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#63958, #11802098, #11802111, … |
| maximal normal subgroup of | C4×#63958, #11802098, #11802111, … |
| maximal quotient of | C2×#10591367, C2×#10591275, C2×#10591722, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7363);