Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×C3×#87547 |
| Fitting | C2×C3×H(7,𝔽2) ⋊ C3 |
| Sylow | C2×H(7,𝔽2) ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C22×C22⋊A4 |
| commutator, cosocle, hypocenter | H(5,𝔽2) | C23×C32 |
| Frattini | C2 | C23×C3×C22⋊A4 |
| Fitting | C2×C3×H(7,𝔽2) | C3 |
| hypercenter | C2×C3×D4 | C22⋊A4 |
| LCS | G ▷ H(5,𝔽2) | |
| UCS | C1 ◁ C22×C3 ◁ C2×C3×D4 | |
21022 conjugacy classes of subgroups; only the 294 normal subgroups are shown.
This group has 21022 conjugacy classes of subgroups — too many to draw. Only its 294 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#11715839, C2×C3×#72209831 |
| maximal normal subgroup of | C2×C3×#11715839 |
Past the SmallGroups library coverage — no SmallGroups id.