Finite Group DatabasebetaFinite Group Databasebeta| order | 7300 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C73 · Schur multiplier (H2) = C5 |
| direct product | C73×#1044 |
| Fitting, socle, Hall | C52×C73 ⋊ C4 |
| derived, Sylow | C52 ⋊ C4×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | #1044 |
| commutator, hypocenter | C52 | C4×C73 |
| Frattini | C1 | G |
| Fitting, socle | C52×C73 | C4 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C73 | |
32 conjugacy classes of subgroups.
730 conjugacy classes — view the full character table.
| maximal subgroup of | C73×#64480, #1044×C73⋊C3, C3×C73×#1044, … |
| maximal normal subgroup of | #1044×C73⋊C3, C3×C73×#1044 |
| maximal quotient of | C3×C73×#1044, C73×C3⋊#1044 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7300, 34);