Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #10593244 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C24×C3 ⋊ C2×D3 |
| derived | C3×C22⋊A4 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C22⋊A4 | C22 |
| Frattini | C22 | D3×S4 |
| Fitting | C24×C3 | C2×D3 |
| socle | C22×C3 | C2×S4 |
| LCS | G ▷ C3×C22⋊A4 | |
| UCS | C1 | |
209 conjugacy classes of subgroups; only the 15 normal subgroups are shown.
This group has 209 conjugacy classes of subgroups — too many to draw. Only its 15 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^2,3^2,2^4|d^a=d^2,e^a=egh,f^a=fg,c^b=c^2,e^b=f,f^b=e,g^b=gh,e^c=f,f^c=ef,g^c=h,h^c=gh24 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5126);