Finite Group DatabasebetaFinite Group Databasebeta| order | 7252 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×Dic37 |
| derived, Sylow | C37 ⋊ C4×C72 |
| Hall | C72×C37 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C72 | D37 |
| commutator, hypocenter | C37 | C4×C72 |
| Frattini | C2 | C72×D37 |
| Fitting, socle | C2×C72×C37 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C72 | |
60 conjugacy classes of subgroups.
1960 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×Dic37⋊C3, C7×#15690920, C7×#15690921, … |
| maximal normal subgroup of | C72×Dic37⋊C3, C7×#15690920, C7×#15690921, … |
| maximal quotient of | C72×Dic111, C3×C72×Dic37, C72×Dic185, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7252, 13);