Finite Group DatabasebetaFinite Group Databasebeta| order | 10276 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D367 |
| unambiguous semidirect product | (D7×C367)⋊C2 |
| unambiguous semidirect product | (C7×D367)⋊C2 |
| unambiguous semidirect product | D2569⋊C2 |
| Fitting, socle, derived, Hall | C7×C367 ⋊ C22 |
| Sylow | C367 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D367 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C367 | C22 |
| LCS | G ▷ C7×C367 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
925 conjugacy classes — view the full character table.
| maximal subgroup of | #29507096⋊C2, #29507097⋊C2, AGL(1,𝔽7)×D367, … |
| maximal normal subgroup of | #29507096⋊C2, #29507097⋊C2, AGL(1,𝔽7)×D367, … |
| maximal quotient of | C3×D7×D367, D21×D367, D7×D1101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10276, 6);