Finite Group DatabasebetaFinite Group Databasebeta| order | 2720 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×D5⋊#3633 |
| Fitting, socle | C2×C5×C17 ⋊ C2×C8 |
| derived, Hall | C5×C17 ⋊ C22×C8 |
| Sylow | C17 ⋊ C2×D5⋊C8 |
| Sylow | C5 ⋊ C22×#3633 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5⋊#3633 |
| commutator, hypocenter | C5×C17 | C22×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C17 | C2×C8 |
| prime radical | C2×D5×D17 | C4 |
| cosocle | #66772 | C23 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C2 | |
152 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 170 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#3633, #72244802 |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#3633 |
| maximal quotient of | #72244802 |
Past the SmallGroups library coverage — no SmallGroups id.