Finite Group DatabasebetaFinite Group Databasebeta| order | 4410 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5×C7 · Schur multiplier (H2) = C3 |
| direct product | C32×C5×C7×D7 |
| Fitting, socle, Hall | C32×C5×C72 ⋊ C2 |
| derived | C7 ⋊ C2×C32×C5×C7 |
| Hall | C32×C72 ⋊ C2×C5 |
| Hall | C5×C72 ⋊ C2×C32 |
| Sylow | C72 ⋊ C2×C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5×C7 | D7 |
| commutator, cosocle, hypocenter | C7 | C2×C32×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C72 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C32×C5×C7 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 630 |
1575 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C7×D7×C25, C32×C52×C7×D7, C32×C5×C7×D35 |
| maximal normal subgroup of | C32×C7×D7×C25, C32×C52×C7×D7 |
| maximal quotient of | C32×C7×D7×C25, C32×C52×C7×D7, C32×C5×C7×D35 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4410, 120);