Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| isoclinism | isoclinic class of C5⋊(#120⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×C5⋊(#120⋊C3) |
| Fitting | C24×C52 ⋊ C2×C3 |
| derived | C24×C5 ⋊ C2×C3×C5 |
| Hall | C5×#4099 ⋊ C3 |
| Sylow | C52 ⋊ #120⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C5⋊(#120⋊C3) |
| commutator, cosocle, hypocenter | C24×C5 | C2×C3×C5 |
| Frattini | C22 | C5×D5×A4 |
| Fitting | C24×C52 | C2×C3 |
| socle | C22×C52 | C2×A4 |
| LCS | G ▷ C24×C5 | |
| UCS | C1 ◁ C5 | |
208 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
130 conjugacy classes — view the full character table.
| maximal subgroup of | #72213644, C5×#1020⋊D5, #72213840 |
| maximal normal subgroup of | #72213644, C5×#1020⋊D5, #72213840 |
Past the SmallGroups library coverage — no SmallGroups id.