Finite Group DatabasebetaFinite Group Databasebeta| order | 7252 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C7 |
| direct product | C37×C7⋊Dic7 |
| unambiguous semidirect product | C7⋊(Dic7×C37) |
| derived, Sylow | C72 ⋊ C4×C37 |
| Hall | C72×C37 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | C7⋊D7 |
| commutator, hypocenter | C72 | C4×C37 |
| Frattini | C2 | C37×C7⋊D7 |
| Fitting, socle | C2×C72×C37 | C2 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C37 | |
60 conjugacy classes of subgroups.
1924 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#10596874, #36344240, #36344241, … |
| maximal normal subgroup of | C37×#10596874, #36344240, #36344241, … |
| maximal quotient of | C37×C3⋊(C7⋊Dic7), C3×C37×C7⋊Dic7, C37×C7⋊Dic35, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7252, 16);