Finite Group DatabasebetaFinite Group Databasebeta| order | 1376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10621900 |
| Fitting | C2×D4×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D43 |
| commutator, cosocle | C2×C43 | C24 |
| Frattini | C2 | C23×D43 |
| Fitting | C2×D4×C43 | C2 |
| socle | C22×C43 | C23 |
| hypercenter | C2×D4 | D43 |
| hypocenter | C43 | C2×#41 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 688 |
230 conjugacy classes — view the full character table.
| maximal subgroup of | #14582871, #14582880, #14582892, … |
| maximal normal subgroup of | #14582871, #14582880, #14582892, … |
| maximal quotient of | C2×#13063281, C2×#13063283, C2×(C22⋊D43)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1376, 188);