Finite Group DatabasebetaFinite Group Databasebeta| order | 10368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C22×C8 |
| direct product | C2×#72220215 |
| derived, Sylow | C34 ⋊ C2×C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #72213199 |
| commutator, hypocenter | C34 | C2×C82 |
| Frattini | C2 | C2×#72213199 |
| Fitting, socle | C22×C34 | C4×C8 |
| prime radical | C22×C3⋊(C3⋊(C3⋊D3)) | C42 |
| cosocle | #13049409 | C23 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C22 | |
1078 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #72252832, #72269065 |
| maximal normal subgroup of | #72252832, #72269065 |
Past the SmallGroups library coverage — no SmallGroups id.