Finite Group DatabasebetaFinite Group Databasebeta| order | 1376 |
| isoclinism | isoclinic class of Dic86 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×Dic86 |
| Sylow | C43 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D43 |
| commutator | C2×C43 | C22×C4 |
| Frattini | C22 | C22×D43 |
| Fitting | C42×C43 | C2 |
| socle, prime radical, cosocle | C22×C43 | C23 |
| hypercenter | C42 | D43 |
| hypocenter | C43 | C4×Q8 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1376 |
356 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14582629, #14582631, C4×#10621883, … |
| maximal normal subgroup of | #14582629, #14582631, C4×#10621883, … |
| maximal quotient of | C4×C4⋊Dic43, C4×Dic43⋊C4, #14582782, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1376, 112);