Finite Group DatabasebetaFinite Group Databasebeta| order | 7910 |
| automorphism | Aut(G) order 10631040 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3955 |
| unambiguous semidirect product | C5⋊D791 |
| unambiguous semidirect product | C7⋊D565 |
| unambiguous semidirect product | C113⋊D35 |
| Fitting, socle, derived, Hall | C5×C7×C113 ⋊ C2 |
| Hall | C7×C113 ⋊ D5 |
| Hall | C5×C113 ⋊ D7 |
| Sylow | C113 ⋊ D35 |
| Hall | C5×C7 ⋊ D113 |
| Sylow | C7 ⋊ D565 |
| Sylow | C5 ⋊ D791 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C113 | C2 |
| LCS | G ▷ C5×C7×C113 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,7,113|b^a=b^4,c^a=c^6,d^a=d^1121979 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D35×D113, D7×D565, D5×D791, … |
| maximal normal subgroup of | D35×D113, D7×D565, D5×D791, … |
| maximal quotient of | Dic3955, C2×D3955, C3×D3955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7910, 9);