Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊Dic385 |
| unambiguous semidirect product | C11⋊(C7⋊Dic35) |
| derived, Hall | C5×C72×C11 ⋊ C4 |
| Hall | C72×C11 ⋊ Dic5 |
| Hall | C5×C72 ⋊ Dic11 |
| Hall | C5×C11 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ Dic55 |
| Sylow | C11 ⋊ C7⋊Dic35 |
| Sylow | C5 ⋊ C7⋊Dic77 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(C7⋊D77) |
| commutator, hypocenter | C5×C72×C11 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C5×C72×C11 | C2 |
| LCS | G ▷ C5×C72×C11 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,7^2,11,2|a^2=f,b^a=b^4,c^a=c^6,d^a=d^6,e^a=e^102698 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11⋊#15668734, C11⋊#15668735, C11⋊(ΓL(1,𝔽8)⋊Dic35), … |
| maximal normal subgroup of | C11⋊#15668734, C11⋊#15668735, C11⋊(ΓL(1,𝔽8)⋊Dic35), … |
| maximal quotient of | C3⋊(C7⋊Dic385), C3×C7⋊Dic385 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 54);