Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C3×C72×#261 |
| Fitting, socle, Hall | C3×C72×C13 ⋊ C4 |
| derived, Sylow | C13 ⋊ C3×C4×C72 |
| Hall | C72×C13 ⋊ C3×C4 |
| Hall | C3×C13 ⋊ C4×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C72 | #261 |
| commutator, hypocenter | C13 | C3×C4×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C4 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C72 | |
120 conjugacy classes of subgroups.
1029 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×#261⋊C9, C7×#15692589, C7×#15692588, … |
| maximal normal subgroup of | C72×#261⋊C9, C7×#15692589, C7×#15692588, … |
| maximal quotient of | C72×C9×#261, C32×C72×#261, C3×C72×C3⋊#261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 313);