Finite Group DatabasebetaFinite Group Databasebeta| order | 6100 |
| isoclinism | isoclinic class of C61⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C4×C5×C61⋊C5 |
| unambiguous semidirect product | (C4×C61)⋊C52 |
| unambiguous semidirect product | (C4×C5×C61)⋊C5 |
| Fitting | C4×C5×C61 ⋊ C5 |
| derived, Sylow | C61 ⋊ C4×C52 |
| Hall | C4×C61 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C5 | C61⋊C5 |
| commutator, hypocenter | C61 | C4×C52 |
| Frattini | C2 | C2×C5×C61⋊C5 |
| Fitting | C4×C5×C61 | C5 |
| socle | C2×C5×C61 | C2×C5 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C4×C5 | |
48 conjugacy classes of subgroups.
340 conjugacy classes — view the full character table.
| maximal subgroup of | C4×C5×(C61⋊C3)⋊C5, C5×Dic3×C61⋊C5, C3×C4×C5×C61⋊C5 |
| maximal normal subgroup of | C4×C5×(C61⋊C3)⋊C5, C3×C4×C5×C61⋊C5 |
| maximal quotient of | C5×Dic3×C61⋊C5, C3×C4×C5×C61⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6100, 25);