Finite Group DatabasebetaFinite Group Databasebeta| order | 7707 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C367 ⋊ C3 |
| Sylow | C367 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C367⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C367 | C3 |
| LCS | G ▷ C7×C367 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3,7,367|b^a=b^4,c^a=c^83859 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21440474, #29507096, #29507100, … |
| maximal normal subgroup of | C2×#21440474, #29507096, #29507100, … |
| maximal quotient of | C2×#21440474, #37528832, C3×#21440474, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7707, 4);