Finite Group DatabasebetaFinite Group Databasebeta| order | 11620 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C83 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic5×C83 |
| derived, Sylow | C5 ⋊ C4×C7×C83 |
| Hall | C5×C7×C83 ⋊ C4 |
| Hall | C5×C83 ⋊ C4×C7 |
| Hall | C5×C7 ⋊ C4×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7×C83 | D5 |
| commutator, hypocenter | C5 | C4×C7×C83 |
| Frattini | C2 | C7×D5×C83 |
| Fitting, socle, prime radical | C2×C5×C7×C83 | C2 |
| cosocle | C2×C5 | C2×C7×C83 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C7×C83 | |
24 conjugacy classes of subgroups.
4648 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×Dic5×C83, C7×Dic15×C83, Dic5×ΓL(1,𝔽8)×C83 |
| maximal normal subgroup of | C3×C7×Dic5×C83, Dic5×ΓL(1,𝔽8)×C83 |
| maximal quotient of | C3×C7×Dic5×C83, C7×Dic15×C83 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11620, 5);