Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| isoclinism | isoclinic class of #64424 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#64424 |
| Fitting, Hall | C72×C25 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C2×C3×C25 |
| Hall | C25×#3861 ⋊ C2 |
| Hall | C25×C7⋊D7 ⋊ C3 |
| Hall | #3861 ⋊ C2×C25 |
| Hall | C7⋊D7 ⋊ C3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #64424 |
| commutator, hypocenter | C72 | C2×C3×C25 |
| Frattini | C5 | C5×#64424 |
| Fitting | C72×C25 | C2×C3 |
| socle | C5×C72 | C2×C3×C5 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C25 | |
120 conjugacy classes of subgroups.
350 conjugacy classes — view the full character table.
| maximal subgroup of | C25×#64423⋊C2, C25×#5997⋊C3, D25×#64424, … |
| maximal normal subgroup of | C25×#64423⋊C2, C25×#5997⋊C3, D25×#64424, … |
| maximal quotient of | C25×#10596874, C2×C25×#64424, C25×#11725077, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 45);