Finite Group DatabasebetaFinite Group Databasebeta| order | 5382 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D299 |
| unambiguous semidirect product | C23⋊(C32×D13) |
| Fitting, socle, Hall | C32×C13×C23 ⋊ C2 |
| derived, Hall | C13×C23 ⋊ C2×C32 |
| Hall | C32×C23 ⋊ D13 |
| Hall | C32×C13 ⋊ D23 |
| Sylow | C23 ⋊ C32×D13 |
| Sylow | C13 ⋊ C32×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D299 |
| commutator, hypocenter | C13×C23 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13×C23 | C2 |
| LCS | G ▷ C13×C23 | |
| UCS | C1 ◁ C32 | |
48 conjugacy classes of subgroups.
1359 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C5×D299, C32×D1495, C3×ΓL(1,𝔽8)⋊D299, … |
| maximal normal subgroup of | C32×C5×D299, C32×C7×D299 |
| maximal quotient of | C32×C5×D299, C32×D1495, C3×ΓL(1,𝔽8)⋊D299, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5382, 24);