Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C22×C3 |
| direct product | C5×C3⋊#5935 |
| Fitting | C3×C5×H(5,𝔽2) ⋊ D3 |
| derived | C3×#997 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C3⋊#1020 |
| commutator, cosocle, hypocenter | C3×#997 | C2×C5 |
| Frattini | C2 | C5×C3⋊#1020 |
| Fitting | C3×C5×H(5,𝔽2) | D3 |
| socle | C2×C3×C5 | #1020 |
| LCS | G ▷ C3×#997 | |
| UCS | C1 ◁ C2×C5 | |
384 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C3⋊#5935, C5×D3×#5935, #72231064 |
| maximal normal subgroup of | D5×C3⋊#5935, C5×D3×#5935, #72231064 |
Past the SmallGroups library coverage — no SmallGroups id.