Finite Group DatabasebetaFinite Group Databasebeta| order | 7164 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C199 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊D3×C199 |
| unambiguous semidirect product | (C2×C3)⋊(D3×C199) |
| Fitting, socle | C2×C32×C199 ⋊ C2 |
| derived, Sylow | C32 ⋊ C22×C199 |
| Hall | C32×C199 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C199 | C3⋊D3 |
| commutator, hypocenter | C32 | C22×C199 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C199 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C199 | |
60 conjugacy classes of subgroups.
2388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×C3⋊D3×C199, C2×C5×C3⋊D3×C199, C2×C3⋊D15×C199 |
| maximal normal subgroup of | C2×C5×C3⋊D3×C199 |
| maximal quotient of | D5×C3⋊D3×C199, C2×C5×C3⋊D3×C199, C2×C3⋊D15×C199 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7164, 48);