Finite Group DatabasebetaFinite Group Databasebeta| order | 7770 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D5×#11715912 |
| unambiguous semidirect product | C5⋊(C2×#11715912) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C37 | C2×C3 |
| LCS | G ▷ C5×C7×C37 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
356 conjugacy classes — view the full character table.
| maximal subgroup of | #29509570, #29509574, #29509582, … |
| maximal normal subgroup of | #29509570, #29509574, #29509582, … |
| maximal quotient of | Dic5×#11715912, C2×D5×#11715912, D5×#14556418, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7770, 36);