Finite Group DatabasebetaFinite Group Databasebeta| order | 5628 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C67 ⋊ C3×C4 |
| Hall | Dic7×C67 ⋊ C3 |
| Hall | #13064104 ⋊ C4 |
| Sylow | C67 ⋊ ΓL(1,𝔽8)⋊C4 |
| Hall | Dic7 ⋊ C67⋊C3 |
| Sylow | C7 ⋊ C4×C67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #14584200 |
| commutator, hypocenter | C7×C67 | C3×C4 |
| Fitting, socle | C2×C7×C67 | C2×C3 |
| LCS | G ▷ C7×C67 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,67,2|a^2=e,c^a=c^6,c^b=c^2,d^b=d^29234 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)⋊C4×C67⋊C3, C3×#19150592, C3⋊#19150592, … |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊C4×C67⋊C3, C3×#19150592, C5×#19150592 |
| maximal quotient of | #30683051, C3×#19150592, C3⋊#19150592, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5628, 20);