Finite Group DatabasebetaFinite Group Databasebeta| order | 4410 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C7 |
| direct product | C3×C72×D15 |
| unambiguous semidirect product | C3⋊(C3×C72×D5) |
| unambiguous semidirect product | C5⋊(C3×D3×C72) |
| Fitting, socle, Hall | C32×C5×C72 ⋊ C2 |
| derived | C3×C5 ⋊ C2×C3×C72 |
| Hall | C32×C72 ⋊ D5 |
| Hall | C5×C72 ⋊ C3×D3 |
| Hall | C32×C5 ⋊ C2×C72 |
| Sylow | C32 ⋊ C72×D5 |
| Sylow | C5 ⋊ C3×D3×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C72 | D15 |
| commutator, cosocle, hypocenter | C3×C5 | C2×C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C72 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C3×C72 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1470 |
1323 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C72×D75, C3×C5×C72×D15, C3×C72×C3⋊(C5⋊D5) |
| maximal normal subgroup of | C3×C5×C72×D15 |
| maximal quotient of | C3×C72×D75, C3×C5×C72×D15, C3×C72×C3⋊(C5⋊D5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4410, 128);