Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C27 |
| direct product | C2×#11710731 |
| Fitting, Sylow | C2×#62817 ⋊ C3 |
| derived | H(3,𝔽4) ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11710731 |
| commutator, cosocle, hypocenter | H(3,𝔽4) | C23×C3 |
| Frattini | C22 | C23×C22⋊A4 |
| Fitting | C2×#62817 | C3 |
| socle | C23 | C22×C22⋊A4 |
| LCS | G ▷ H(3,𝔽4) | |
| UCS | C1 ◁ C2 | |
15780 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 15780 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(2,ℤ/4), C2×#72215828, D5×#11710731, … |
| maximal normal subgroup of | C2×AGL(2,ℤ/4), C2×#72215828, C4×#11710731, … |
| maximal quotient of | C2×#72231801, D5×#11710731, C4×#11710731, … |
Past the SmallGroups library coverage — no SmallGroups id.