Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| isoclinism | isoclinic class of C3⋊D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C37 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C37×C3⋊D15 |
| unambiguous semidirect product | (C2×C3)⋊(D15×C37) |
| unambiguous semidirect product | (C2×C5)⋊(C3⋊D3×C37) |
| Fitting, socle | C2×C32×C5×C37 ⋊ C2 |
| derived, Hall | C32×C5 ⋊ C22×C37 |
| Hall | C32×C5×C37 ⋊ C22 |
| Hall | C32×C37 ⋊ C2×D5 |
| Hall | C5×C37 ⋊ C2×C3⋊D3 |
| Sylow | C32 ⋊ C2×D5×C37 |
| Sylow | C5 ⋊ C2×C3⋊D3×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | C3⋊D15 |
| commutator, hypocenter | C32×C5 | C22×C37 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C5×C37 | C2 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C2×C37 | |
120 conjugacy classes of subgroups.
1776 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C37×C3⋊D75, D5×C37×C3⋊D15, C2×C5×C37×C3⋊D15, … |
| maximal normal subgroup of | C2×C5×C37×C3⋊D15 |
| maximal quotient of | C2×C37×C3⋊D75, D5×C37×C3⋊D15, C2×C5×C37×C3⋊D15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 172);