Finite Group DatabasebetaFinite Group Databasebeta| order | 7972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C1993 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1993 | C4 |
| LCS | G ▷ C1993 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,1993|a^2=b,c^a=c^834,c^b=c^1992502 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22547539, #30630009, #22547539⋊C3, … |
| maximal normal subgroup of | C2×#22547539, #30630009, #22547539⋊C3, … |
| maximal quotient of | #30630007, C2×#22547539, C3×#22547539, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7972, 3);