Finite Group DatabasebetaFinite Group Databasebeta| order | 6573 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C313 ⋊ C3 |
| Sylow | C313 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C313⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C313 | C3 |
| LCS | G ▷ C7×C313 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3,7,313|b^a=b^4,c^a=c^98733 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20267161, #27190374, #27190378, … |
| maximal normal subgroup of | C2×#20267161, #27190374, #27190378, … |
| maximal quotient of | C2×#20267161, #34089347, C3×#20267161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6573, 4);