Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#63914 |
| Sylow | C32 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D32 |
| commutator, cosocle | C22×C32 | C24 |
| Frattini | C22 | C22×D32 |
| Fitting | C22×C32×C4 | C22 |
| socle | C23×C32 | C23 |
| hypercenter | C22×C4 | D32 |
| hypocenter | C32 | C2×#127 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
1050 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10590037, #11776275, #11776277, … |
| maximal normal subgroup of | C2×#10590037, #11776275, #11776277, … |
| maximal quotient of | C2×#10591359, C2×#10591385, C2×#10591323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6901);