Finite Group DatabasebetaFinite Group Databasebeta| order | 3136 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×#11716115 |
| Fitting | C24×C72 ⋊ C22 |
| Sylow | C72 ⋊ C23×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D72 |
| commutator, cosocle | C2×C72 | C25 |
| Frattini | C2 | C23×D72 |
| Fitting | C24×C72 | C22 |
| socle | C23×C72 | C23 |
| hypercenter | C24 | D72 |
| hypocenter | C72 | C23×D4 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C23 ◁ C24 | |
3846 conjugacy classes of subgroups; only the 608 normal subgroups are shown.
This group has 3846 conjugacy classes of subgroups — too many to draw. Only its 608 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
304 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3×#11716115, C22×#72210376, C2×#72214319 |
| maximal normal subgroup of | C22×#72210376, C2×#72214319 |
| maximal quotient of | C2×D3×#11716115, C2×#72214529 |
Past the SmallGroups library coverage — no SmallGroups id.