Finite Group DatabasebetaFinite Group Databasebeta| order | 10948 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D391 |
| unambiguous semidirect product | (C2×C17)⋊(C7×D23) |
| unambiguous semidirect product | (C2×C23)⋊(C7×D17) |
| Fitting, socle | C2×C7×C17×C23 ⋊ C2 |
| derived, Hall | C17×C23 ⋊ C22×C7 |
| Hall | C7×C17×C23 ⋊ C22 |
| 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 | C2×C7 | D391 |
| commutator, cosocle, hypocenter | C17×C23 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C17×C23 | C2 |
| LCS | G ▷ C17×C23 | |
| UCS | C1 ◁ C2×C7 | |
40 conjugacy classes of subgroups.
2758 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×ΓL(1,𝔽8)×D391, D3×C7×D391, C2×C3×C7×D391, … |
| maximal normal subgroup of | C2×ΓL(1,𝔽8)×D391, C2×C3×C7×D391 |
| maximal quotient of | D3×C7×D391, C2×C3×C7×D391, C2×C7×D1173 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10948, 25);