Finite Group DatabasebetaFinite Group Databasebeta| order | 10948 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C17 · Schur multiplier (H2) = C1 |
| direct product | C7×C17×Dic23 |
| unambiguous semidirect product | C23⋊(C4×C7×C17) |
| derived, Sylow | C23 ⋊ C4×C7×C17 |
| Hall | C7×C17×C23 ⋊ C4 |
| Hall | C17×C23 ⋊ C4×C7 |
| Hall | C7×C23 ⋊ C4×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7×C17 | D23 |
| commutator, hypocenter | C23 | C4×C7×C17 |
| Frattini | C2 | C7×C17×D23 |
| Fitting, socle, prime radical | C2×C7×C17×C23 | C2 |
| cosocle | C2×C23 | C2×C7×C17 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C2×C7×C17 | |
24 conjugacy classes of subgroups.
3094 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×C17×Dic23, C7×C17×Dic69, C17×ΓL(1,𝔽8)×Dic23 |
| maximal normal subgroup of | C3×C7×C17×Dic23, C17×ΓL(1,𝔽8)×Dic23 |
| maximal quotient of | C3×C7×C17×Dic23, C7×C17×Dic69 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10948, 2);