Finite Group DatabasebetaFinite Group Databasebeta| order | 10948 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | D7×C23×D17 |
| unambiguous semidirect product | (D7×C17)⋊(C2×C23) |
| unambiguous semidirect product | (C7×D17)⋊(C2×C23) |
| unambiguous semidirect product | D119⋊(C2×C23) |
| Fitting, socle, Hall | C7×C17×C23 ⋊ C22 |
| derived, Hall | C7×C17 ⋊ C22×C23 |
| Hall | C17×C23 ⋊ C2×D7 |
| Hall | C7×C23 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D7×C23 |
| Sylow | C7 ⋊ C2×C23×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D7×D17 |
| commutator, cosocle, hypocenter | C7×C17 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C23 | C22 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C23 | |
40 conjugacy classes of subgroups.
1150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×D17×AGL(1,𝔽7), C3×D7×C23×D17, C23×D17×D21, … |
| maximal normal subgroup of | C23×D17×AGL(1,𝔽7), C3×D7×C23×D17 |
| maximal quotient of | C3×D7×C23×D17, C23×D17×D21, D7×C23×D51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10948, 17);