Finite Group DatabasebetaFinite Group Databasebeta| order | 9680 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×#72213666 |
| Hall | C2×#11757246 ⋊ C5 |
| Hall | #10597243 ⋊ C2×D4 |
| Sylow | C112 ⋊ C2×C5×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #11925892⋊C2 |
| commutator, cosocle | C2×C112 | C23×C5 |
| Frattini | C2 | C2×#11925892⋊C2 |
| Fitting, socle | C22×C112 | C22×C5 |
| hypocenter | C112 | C2×C5×D4 |
| LCS | G ▷ C2×C112 ▷ C112 | |
| UCS | C1 ◁ C22 | |
376 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 376 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.
86 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72213693, #72222629, D3×#72213666 |
| maximal normal subgroup of | C2×#72213693, #72222629 |
| maximal quotient of | #72222610, D3×#72213666 |
Past the SmallGroups library coverage — no SmallGroups id.