Finite Group DatabasebetaFinite Group Databasebeta| order | 10948 |
| isoclinism | isoclinic class of D119 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×Dic119 |
| unambiguous semidirect product | C7⋊(C23×Dic17) |
| derived, Hall | C7×C17 ⋊ C4×C23 |
| Hall | C7×C17×C23 ⋊ C4 |
| Hall | C17×C23 ⋊ Dic7 |
| Hall | C7×C23 ⋊ Dic17 |
| Sylow | C17 ⋊ C23×Dic7 |
| Sylow | C7 ⋊ C23×Dic17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D119 |
| commutator, hypocenter | C7×C17 | C4×C23 |
| Frattini | C2 | C23×D119 |
| Fitting, socle, prime radical | C2×C7×C17×C23 | C2 |
| cosocle | C2×C7×C17 | C2×C23 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C2×C23 | |
24 conjugacy classes of subgroups.
2806 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C23×Dic119, C23×Dic357, C23×ΓL(1,𝔽8)⋊Dic17 |
| maximal normal subgroup of | C3×C23×Dic119, C23×ΓL(1,𝔽8)⋊Dic17 |
| maximal quotient of | C3×C23×Dic119, C23×Dic357 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10948, 7);