Finite Group DatabasebetaFinite Group Databasebeta| order | 7252 |
| isoclinism | isoclinic class of #5997 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C7 |
| direct product | C37×#5997 |
| Fitting, socle, Hall | C72×C37 ⋊ C4 |
| derived, Sylow | C72 ⋊ C4×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | #5997 |
| commutator, hypocenter | C72 | C4×C37 |
| Frattini | C1 | G |
| Fitting, socle | C72×C37 | C4 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C37 | |
28 conjugacy classes of subgroups.
592 conjugacy classes — view the full character table.
| maximal subgroup of | C37×#10596885, C37⋊C3×#5997, C37×#5997⋊C3, … |
| maximal normal subgroup of | C37⋊C3×#5997, C37×#5997⋊C3, #36344318, … |
| maximal quotient of | C3×C37×#5997, C37×C3⋊#5997, C5×C37×#5997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7252, 27);