Finite Group DatabasebetaFinite Group Databasebeta| order | 10972 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D13×D211 |
| unambiguous semidirect product | (D13×C211)⋊C2 |
| unambiguous semidirect product | (C13×D211)⋊C2 |
| unambiguous semidirect product | D2743⋊C2 |
| Fitting, socle, derived, Hall | C13×C211 ⋊ C22 |
| Sylow | C211 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×D211 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C211 | C22 |
| LCS | G ▷ C13×C211 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
856 conjugacy classes — view the full character table.
| maximal subgroup of | #30657972⋊C2, #30657971⋊C2, D13⋊C3×D211, … |
| maximal normal subgroup of | #30657972⋊C2, #30657971⋊C2, D13⋊C3×D211, … |
| maximal quotient of | C3×D13×D211, D39×D211, D13×D633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10972, 8);