Finite Group DatabasebetaFinite Group Databasebeta| order | 7268 |
| isoclinism | isoclinic class of D79 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×Dic79 |
| unambiguous semidirect product | C79⋊(C4×C23) |
| derived, Sylow | C79 ⋊ C4×C23 |
| Hall | C23×C79 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D79 |
| commutator, hypocenter | C79 | C4×C23 |
| Frattini | C2 | C23×D79 |
| Fitting, socle | C2×C23×C79 | C2 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C2×C23 | |
12 conjugacy classes of subgroups.
1886 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C23×Dic79, C23×Dic237, C23×(C79⋊C3)⋊C4, … |
| maximal normal subgroup of | C3×C23×Dic79, C23×(C79⋊C3)⋊C4, C5×C23×Dic79 |
| maximal quotient of | C3×C23×Dic79, C23×Dic237, C5×C23×Dic79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7268, 3);