Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| isoclinism | isoclinic class of #67138 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C5×#67140 |
| Hall | C32×C52 ⋊ C2×D4 |
| Sylow | C52 ⋊ C2×C4⋊(C3⋊D3) |
| Sylow | C32 ⋊ C2×C5×C22⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | D5×C3⋊D3 |
| commutator, cosocle | C2×C32×C5 | C23×C5 |
| Frattini | C2 | C2×C5×D5×C3⋊D3 |
| Fitting, socle | C22×C32×C52 | C22 |
| hypocenter | C32×C5 | C2×C5×D4 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22×C5 | |
840 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 360 |
450 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72229316, C2×C5×C3⋊D3×C22⋊D5, C2×#72231468 |
| maximal normal subgroup of | C2×#72229316, C2×C5×C3⋊D3×C22⋊D5, C2×#72231468 |
Past the SmallGroups library coverage — no SmallGroups id.