Finite Group DatabasebetaFinite Group Databasebeta| order | 10948 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D17×D23 |
| unambiguous semidirect product | (C23×D17)⋊(C2×C7) |
| unambiguous semidirect product | (C17×D23)⋊(C2×C7) |
| unambiguous semidirect product | D391⋊(C2×C7) |
| Fitting, socle, Hall | C7×C17×C23 ⋊ C22 |
| derived, Hall | C17×C23 ⋊ C22×C7 |
| Hall | C7×C23 ⋊ C2×D17 |
| Hall | C7×C17 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×C7×D17 |
| Sylow | C17 ⋊ C2×C7×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D17×D23 |
| commutator, cosocle, hypocenter | C17×C23 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C23 | C22 |
| LCS | G ▷ C17×C23 | |
| UCS | C1 ◁ C7 | |
40 conjugacy classes of subgroups.
910 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×D17×D23, C3×C7×D17×D23, C7×D23×D51, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×D17×D23, C3×C7×D17×D23 |
| maximal quotient of | C3×C7×D17×D23, C7×D23×D51, C7×D17×D69, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10948, 12);