Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7 · Schur multiplier (H2) = C2 |
| direct product | C5×C7×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C5×C7 | A5 |
| commutator, hypocenter | A5 | C5×C7 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C5×C7 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 175 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C49×A5, C5×C72×A5, C5×C7×C11×A5, … |
| maximal normal subgroup of | C5×C49×A5, C5×C72×A5, C5×C7×C11×A5, … |
| maximal quotient of | C5×C49×A5, C5×C72×A5, C5×C7×C11×A5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 165);