Finite Group DatabasebetaFinite Group Databasebeta| order | 10240 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C26 |
| direct product | C2×#72210041 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C22 | #72209701 |
| commutator, cosocle, hypocenter | #72210028 | C22 |
| Frattini | C2 | C2×#72209701 |
| Fitting | C2×H(9,𝔽2) | D5 |
| prime radical | C2×#72210028 | C2 |
| LCS | G ▷ #72210028 | |
| UCS | C1 ◁ C22 | |
Only the 22 normal subgroups are shown; non-normal subgroups are omitted.
Only the group's 22 normal subgroups are shown; non-normal subgroups are omitted.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
112 conjugacy classes — view the full character table.
| maximal subgroup of | #72257978 |
Past the SmallGroups library coverage — no SmallGroups id.