Finite Group DatabasebetaFinite Group Databasebeta| order | 5572 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic199 |
| unambiguous semidirect product | C199⋊(C4×C7) |
| derived, Sylow | C199 ⋊ C4×C7 |
| Hall | C7×C199 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D199 |
| commutator, hypocenter | C199 | C4×C7 |
| Frattini | C2 | C7×D199 |
| Fitting, socle | C2×C7×C199 | C2 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C2×C7 | |
12 conjugacy classes of subgroups.
1414 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×Dic199, C7×Dic597, C7×(C199⋊C3)⋊C4, … |
| maximal normal subgroup of | C3×C7×Dic199, C7×(C199⋊C3)⋊C4, ΓL(1,𝔽8)×Dic199, … |
| maximal quotient of | C3×C7×Dic199, C7×Dic597, C5×C7×Dic199, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5572, 3);