Finite Group DatabasebetaFinite Group Databasebeta| order | 1376 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D344 |
| Fitting | C2×C8×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D172 |
| commutator, cosocle | C4×C43 | C23 |
| Frattini | C4 | C22×D43 |
| Fitting | C2×C8×C43 | C2 |
| socle | C22×C43 | D4 |
| hypercenter | C2×C8 | D43 |
| hypocenter | C43 | C2×D8 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 688 |
350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14582699, #14582701, #14582711, … |
| maximal normal subgroup of | #14582699, #14582701, #14582711, … |
| maximal quotient of | C2×#13063247, C2×#13063259, C4×D344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1376, 157);