Finite Group DatabasebetaFinite Group Databasebeta| order | 6100 |
| isoclinism | isoclinic class of D61 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C52×D61 |
| Fitting, socle | C2×C52×C61 ⋊ C2 |
| derived, Sylow | C61 ⋊ C22×C52 |
| Hall | C52×C61 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | D61 |
| commutator, hypocenter | C61 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C61 | C2 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C52 | |
80 conjugacy classes of subgroups.
1600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C52×D61⋊C3, C2×D61⋊(C52⋊C3), C2×C52⋊C3×D61, … |
| maximal normal subgroup of | C2×C52×D61⋊C3, C2×D61⋊(C52⋊C3), C2×C52⋊C3×D61, … |
| maximal quotient of | C52×D3×D61, C2×C52×D183, C2×C3×C52×D61 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6100, 70);