Finite Group DatabasebetaFinite Group Databasebeta| order | 7869 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C43×C61 ⋊ C3 |
| Sylow | C61 ⋊ C43⋊C3 |
| Sylow | C43 ⋊ C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C43×C61 | C3 |
| LCS | G ▷ C43×C61 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3,43,61|b^a=b^36,c^a=c^13877 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21463501, #30628680, #30628684, … |
| maximal normal subgroup of | C2×#21463501, #30628680, #30628684, … |
| maximal quotient of | C2×#21463501, #37556290, C3×#21463501, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7869, 4);