Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| isoclinism | isoclinic class of C13⋊D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C13 |
| direct product | C2×C32×C13⋊D13 |
| Fitting, socle | C2×C32×C132 ⋊ C2 |
| derived, Sylow | C132 ⋊ C22×C32 |
| Hall | C32×C132 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | C13⋊D13 |
| commutator, hypocenter | C132 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C132 | C2 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C2×C32 | |
480 conjugacy classes of subgroups.
1548 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D5×C13⋊D13, C2×C32×C5×C13⋊D13, C2×C32×C5⋊(C13⋊D13) |
| maximal normal subgroup of | C2×C32×C5×C13⋊D13 |
| maximal quotient of | C32×D5×C13⋊D13, C2×C32×C5×C13⋊D13, C2×C32×C5⋊(C13⋊D13) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 297);