Finite Group DatabasebetaFinite Group Databasebeta| order | 5404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#11715871 |
| Fitting, socle, Hall | C7×C193 ⋊ C4 |
| derived, Sylow | C193 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #11715871 |
| commutator, hypocenter | C193 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C193 | C4 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C7 | |
12 conjugacy classes of subgroups.
364 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#11715871⋊C3, #30633870, #30633871, … |
| maximal normal subgroup of | C7×#11715871⋊C3, #30633870, #30633871, … |
| maximal quotient of | C3×C7×#11715871, C7×C3⋊#11715871, C5×C7×#11715871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5404, 6);