Finite Group DatabasebetaFinite Group Databasebeta| order | 5796 |
| isoclinism | isoclinic class of D161 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×D161 |
| unambiguous semidirect product | (C2×C23)⋊(C32×D7) |
| Fitting, socle | C2×C32×C7×C23 ⋊ C2 |
| derived, Hall | C7×C23 ⋊ C22×C32 |
| Hall | C32×C7×C23 ⋊ C22 |
| Hall | C32×C23 ⋊ C2×D7 |
| Hall | C32×C7 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×C32×D7 |
| Sylow | C7 ⋊ C2×C32×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D161 |
| commutator, hypocenter | C7×C23 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C7×C23 | C2 |
| LCS | G ▷ C7×C23 | |
| UCS | C1 ◁ C2×C32 | |
120 conjugacy classes of subgroups.
1476 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D5×D161, C2×C32×C5×D161, C2×C32×D805 |
| maximal normal subgroup of | C2×C32×C5×D161 |
| maximal quotient of | C32×D5×D161, C2×C32×C5×D161, C2×C32×D805 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5796, 109);