Finite Group DatabasebetaFinite Group Databasebeta| order | 7828 |
| isoclinism | isoclinic class of D103 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×Dic103 |
| unambiguous semidirect product | C103⋊(C4×C19) |
| derived, Sylow | C103 ⋊ C4×C19 |
| Hall | C19×C103 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | D103 |
| commutator, hypocenter | C103 | C4×C19 |
| Frattini | C2 | C19×D103 |
| Fitting, socle | C2×C19×C103 | C2 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C2×C19 | |
12 conjugacy classes of subgroups.
2014 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C19×Dic103, C19×Dic309, C19×(C103⋊C3)⋊C4, … |
| maximal normal subgroup of | C3×C19×Dic103, C19×(C103⋊C3)⋊C4, C19⋊C3×Dic103, … |
| maximal quotient of | C3×C19×Dic103, C19×Dic309 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7828, 3);