Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| isoclinism | isoclinic class of D55 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×Dic55 |
| unambiguous semidirect product | C11⋊(C72×Dic5) |
| derived, Hall | C5×C11 ⋊ C4×C72 |
| Hall | C5×C72×C11 ⋊ C4 |
| Hall | C72×C11 ⋊ Dic5 |
| Hall | C5×C72 ⋊ Dic11 |
| Sylow | C11 ⋊ C72×Dic5 |
| Sylow | C5 ⋊ C72×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C72 | D55 |
| commutator, hypocenter | C5×C11 | C4×C72 |
| Frattini | C2 | C72×D55 |
| Fitting, socle, prime radical | C2×C5×C72×C11 | C2 |
| cosocle | C2×C5×C11 | C2×C72 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C2×C72 | |
120 conjugacy classes of subgroups.
2842 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×ΓL(1,𝔽8)×Dic55, #3861×Dic55, #3862×Dic55, … |
| maximal normal subgroup of | C7×ΓL(1,𝔽8)×Dic55, #3861×Dic55, #3862×Dic55, … |
| maximal quotient of | C72×Dic165, C3×C72×Dic55 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 50);