Finite Group DatabasebetaFinite Group Databasebeta| order | 7300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#13091735 |
| Fitting, socle, Hall | C52×C73 ⋊ C4 |
| derived | C5×C73 ⋊ C4×C5 |
| Sylow | C73 ⋊ C5×Dic5 |
| Sylow | C52 ⋊ #64408 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #13091735 |
| commutator, hypocenter | C5×C73 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C73 | C4 |
| LCS | G ▷ C5×C73 | |
| UCS | C1 ◁ C5 | |
32 conjugacy classes of subgroups.
490 conjugacy classes — view the full character table.
| maximal subgroup of | #36346460, C5×#13091735⋊C3, C3×C5×#13091735, … |
| maximal normal subgroup of | C5×#13091735⋊C3, C3×C5×#13091735 |
| maximal quotient of | C3×C5×#13091735, C5×C3⋊#13091735 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7300, 28);