Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#63553 |
| derived, Sylow | C32 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D32 |
| commutator, hypocenter | C32 | C2×C4×C8 |
| Frattini | C2×C4 | C2×D32 |
| Fitting | C22×C32×C4 | C22 |
| socle, prime radical | C23×C32 | C2×C4 |
| cosocle | C2×C32×C4 | C23 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C22×C4 | |
378 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 378 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) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #11770778, #11770799, C2×#10590030, … |
| maximal normal subgroup of | #11770778, #11770799, C2×#10590030, … |
| maximal quotient of | C2×C3⋊C82, C2×#10589079, #11773548, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2940);