Finite Group DatabasebetaFinite Group Databasebeta| order | 1376 |
| isoclinism | isoclinic class of D43 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D43 |
| unambiguous semidirect product | C43⋊C25 |
| unambiguous semidirect product | (C2×C43)⋊C24 |
| Fitting, socle | C24×C43 ⋊ C2 |
| derived, Sylow | C43 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D43 |
| commutator, cosocle, hypocenter | C43 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C43 | C2 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C24 | |
748 conjugacy classes of subgroups.
| transitive degree | μt(G) = 688 |
368 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14582754, C2×C22⋊C4×D43, C22×(C2×D43)⋊C4, … |
| maximal normal subgroup of | #14582754, C2×C22⋊C4×D43, C22×(C2×D43)⋊C4, … |
| maximal quotient of | C23×C4×D43, C24×Dic43, C22×D4×D43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1376, 195);