Finite Group DatabasebetaFinite Group Databasebeta| order | 1083 |
| isoclinism | isoclinic class of #11762245 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C192 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C192 | C3 |
| LCS | G ▷ C192 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 361 |
Polycyclic presentation:
3,19^2|b^a=b^7,c^a=c^7123 conjugacy classes — view the full character table.
| maximal subgroup of | #14524206, #14524208, C2×#11762245, … |
| maximal normal subgroup of | #14524206, #14524208, C2×#11762245, … |
| maximal quotient of | C2×#11762245, #15692429, C3×#11762245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1083, 4);