Finite Group DatabasebetaFinite Group Databasebeta| order | 7012 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C1753 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1753 | C4 |
| LCS | G ▷ C1753 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,1753|a^2=b,c^a=c^713,c^b=c^1752442 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20296241, #28380415, #20296241⋊C3, … |
| maximal normal subgroup of | C2×#20296241, #28380415, #20296241⋊C3, … |
| maximal quotient of | #28380413, C2×#20296241, C3×#20296241, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7012, 3);