Finite Group DatabasebetaFinite Group Databasebeta| order | 7300 |
| isoclinism | isoclinic class of #64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#64408 |
| Fitting, Hall | C25×C73 ⋊ C4 |
| derived, Sylow | C73 ⋊ C4×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #64408 |
| commutator, hypocenter | C73 | C4×C25 |
| Frattini | C5 | C5×#64408 |
| Fitting | C25×C73 | C4 |
| socle | C5×C73 | C4×C5 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C25 | |
18 conjugacy classes of subgroups.
550 conjugacy classes — view the full character table.
| maximal subgroup of | C25×#64408⋊C3, C3×C25×#64408, C25×C3⋊#64408 |
| maximal normal subgroup of | C25×#64408⋊C3, C3×C25×#64408 |
| maximal quotient of | C3×C25×#64408, C25×C3⋊#64408 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7300, 6);