Finite Group DatabasebetaFinite Group Databasebeta| order | 1384 |
| isoclinism | isoclinic class of #10621924 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#10621924 |
| unambiguous semidirect product | D173⋊C4 |
| Fitting, socle | C2×C173 ⋊ C4 |
| derived, Sylow | C173 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10621924 |
| commutator, hypocenter | C173 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C173 | C4 |
| prime radical | C2×D173 | C2 |
| cosocle | D173 | C22 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 346 |
94 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#10621924, C22⋊#10621924, C4⋊#10621924, … |
| maximal normal subgroup of | C4×#10621924, C22⋊#10621924, C4⋊#10621924, … |
| maximal quotient of | C4×#10621924, C22⋊#10621924, C4⋊#10621924, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1384, 14);