Finite Group DatabasebetaFinite Group Databasebeta| order | 4410 |
| isoclinism | isoclinic class of #3861 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C2×C3×C5×#3861 |
| Fitting, socle | C2×C3×C5×C72 ⋊ C3 |
| derived, Sylow | C72 ⋊ C2×C32×C5 |
| Hall | C2×C5×C72 ⋊ C32 |
| Hall | C5×C72 ⋊ C2×C32 |
| Hall | C2×C72 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | #3861 |
| commutator, cosocle, hypocenter | C72 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C72 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C3×C5 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1470 |
570 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C25×#3861, C3×C5×D5×#3861, C2×C3×C52×#3861 |
| maximal normal subgroup of | C2×C3×C25×#3861, C2×C3×C52×#3861 |
| maximal quotient of | C2×C3×C25×#3861, C3×C5×D5×#3861, C2×C3×C52×#3861 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4410, 118);