Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#11924181 |
| Hall | C2×#87641 ⋊ C3 |
| Hall | #3862 ⋊ C2×D4 |
| Sylow | C72 ⋊ C2×C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #64422⋊C2 |
| commutator, cosocle | C2×C72 | C23×C3 |
| Frattini | C2 | C2×#64422⋊C2 |
| Fitting, socle | C22×C72 | C22×C3 |
| hypocenter | C72 | C2×C3×D4 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C22 | |
232 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
58 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72222022, C2×#72222015, #72246021, … |
| maximal normal subgroup of | C2×#72222022, C2×#72222015, #72246021, … |
| maximal quotient of | #72245114, #72246058, #72246134 |
Past the SmallGroups library coverage — no SmallGroups id.