Finite Group DatabasebetaFinite Group Databasebeta| order | 10376 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C22×D1297 |
| unambiguous semidirect product | C1297⋊C23 |
| unambiguous semidirect product | (C2×C1297)⋊C22 |
| Fitting, socle | C22×C1297 ⋊ C2 |
| derived, Sylow | C1297 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D1297 |
| commutator, cosocle, hypocenter | C1297 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C22×C1297 | C2 |
| LCS | G ▷ C1297 | |
| UCS | C1 ◁ C22 | |
32 conjugacy classes of subgroups.
2600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35209232, C2×C4×D1297, D4×D1297, … |
| maximal normal subgroup of | #35209232, C2×C4×D1297, D4×D1297, … |
| maximal quotient of | C2×C4×D1297, C22×Dic1297, D4×D1297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10376, 12);