Finite Group Databasebeta

← Prev (#24924751) Next (#24924753) →

C2×C7×D7×C11⋊C5 #24924752

order10780
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D7×C11⋊C5
unambiguous semidirect productC7⋊(C22×C7×C11⋊C5)
unambiguous semidirect product(C2×C7)⋊(C2×C7×C11⋊C5)
unambiguous semidirect product(C2×C11×D7)⋊(C5×C7)
unambiguous semidirect product(C2×C7×C11×D7)⋊C5

Splittings

Fitting, socleC2×C72×C11 ⋊ C2×C5
derivedC7×C11 ⋊ C22×C5×C7
HallC72×C11⋊C5 ⋊ C22
HallC2×C7×C11×D7 ⋊ C5
HallC72×C11 ⋊ C22×C5
SylowC72 ⋊ C22×C11⋊C5
SylowC11 ⋊ C2×C5×C7×D7

Subgroups

subgroupG/H
center, hypercenterC2×C7D7×C11⋊C5
commutator, cosocle, hypocenterC7×C11C22×C5×C7
FrattiniC1G
Fitting, socleC2×C72×C11C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C7

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

490 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C11⋊C5×#64418, C2×C7×AGL(1,𝔽7)×C11⋊C5, C2×D7×ΓL(1,𝔽8)×C11⋊C5, …
maximal normal subgroup ofC2×C7×AGL(1,𝔽7)×C11⋊C5, C2×D7×ΓL(1,𝔽8)×C11⋊C5, C2×C11⋊C5×#64423, …
maximal quotient ofD3×C7×D7×C11⋊C5, C2×C3×C7×D7×C11⋊C5, C2×C7×D21×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 65);