Finite Group DatabasebetaFinite Group Databasebeta| order | 1448 |
| isoclinism | isoclinic class of #10624382 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#10624382 |
| unambiguous semidirect product | D181⋊C4 |
| Fitting, socle | C2×C181 ⋊ C4 |
| derived, Sylow | C181 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10624382 |
| commutator, hypocenter | C181 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C181 | C4 |
| prime radical | C2×D181 | C2 |
| cosocle | D181 | C22 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 362 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#10624382, C22⋊#10624382, C4⋊#10624382, … |
| maximal normal subgroup of | C4×#10624382, C22⋊#10624382, C4⋊#10624382, … |
| maximal quotient of | C4×#10624382, C22⋊#10624382, C4⋊#10624382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1448, 14);