Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×#3811 |
| Fitting | C24×C32 ⋊ C22 |
| Sylow | C32 ⋊ C23×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D32 |
| commutator, cosocle | C2×C32 | C25 |
| Frattini | C2 | C23×D32 |
| Fitting | C24×C32 | C22 |
| socle | C23×C32 | C23 |
| hypercenter | C24 | D32 |
| hypocenter | C32 | C23×D4 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C24 | |
3098 conjugacy classes of subgroups; only the 608 normal subgroups are shown.
This group has 3098 conjugacy classes of subgroups — too many to draw. Only its 608 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #11773287, #11784603, #11784608, … |
| maximal normal subgroup of | #11773287, #11784603, #11784608, … |
| maximal quotient of | C22×#63921, C22×#63974, C22×#63883, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8589);