Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C3×C4 |
| direct product | C16×C3⋊Dic3 |
| derived, Sylow | C32 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | C3⋊D3 |
| commutator, hypocenter | C32 | C4×C16 |
| Frattini | C2×C8 | C2×C3⋊D3 |
| Fitting | C2×C32×C16 | C2 |
| socle, prime radical | C22×C32 | C2×C8 |
| cosocle | C2×C32×C8 | C22 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C16 | |
174 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#622, #11771299, #11771313, … |
| maximal normal subgroup of | C16×#622, #11771299, #11771313, … |
| maximal quotient of | C16×C3⋊(C3⋊C8), #11771309, #11772258, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1248);