Finite Group DatabasebetaFinite Group Databasebeta| order | 10675 |
| isoclinism | isoclinic class of C61⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C7 · Schur multiplier (H2) = C5 |
| Fitting, socle | C5×C7×C61 ⋊ C5 |
| derived, Sylow | C61 ⋊ C52×C7 |
| Hall | C7×C61 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | C61⋊C5 |
| commutator, cosocle, hypocenter | C61 | C52×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C61 | C5 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C5×C7 | |
32 conjugacy classes of subgroups.
595 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C7×D61⋊C5, C5×C7⋊(D61⋊C5), C5×D7×C61⋊C5, … |
| maximal normal subgroup of | C5×C7×D61⋊C5, C5×C7⋊(D61⋊C5), C5×D7×C61⋊C5, … |
| maximal quotient of | C2×C5×C7×C61⋊C5, C3×C5×C7×C61⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10675, 4);