Finite Group DatabasebetaFinite Group Databasebeta| order | 7947 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C883 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C883 | C9 |
| LCS | G ▷ C883 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
3^2,883|a^3=b,c^a=c^560,c^b=c^545107 conjugacy classes — view the full character table.
| maximal subgroup of | #22547287⋊C2, C2×#22547287, C3×#22547287, … |
| maximal normal subgroup of | #22547287⋊C2, C2×#22547287, C3×#22547287 |
| maximal quotient of | C2×#22547287, #37558636, C3×#22547287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7947, 3);