Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #625 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#3722 |
| Sylow | C32 ⋊ C22×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D32 |
| commutator | C2×C32 | C23×C4 |
| Frattini | C22 | C22×D32 |
| Fitting, socle | C24×C32 | C22 |
| prime radical | C24×C3⋊D3 | C2 |
| cosocle | C22×C32 | C24 |
| hypocenter | C32 | C22×C22⋊C4 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C24 | |
1722 conjugacy classes of subgroups; only the 392 normal subgroups are shown.
This group has 1722 conjugacy classes of subgroups — too many to draw. Only its 392 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #11773162, #11773164, #11773264, … |
| maximal normal subgroup of | #11773162, #11773164, #11773264, … |
| maximal quotient of | C22×#63579, C2×C4×#3722, C2×#10591714, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7368);