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C2×C11⋊C5×C7⋊D7 #24924754

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

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×C7⋊D7
commutator, cosocle, hypocenterC72×C11C22×C5
FrattiniC1G
Fitting, socleC2×C72×C11C2×C5
LCSG ▷ C72×C11
UCSC1 ◁ C2

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C11⋊C5×ΓL(1,𝔽8)⋊D7, C2×C11⋊C5×#64424, C2×C11⋊C5×#64425, …
maximal normal subgroup ofC2×C11⋊C5×ΓL(1,𝔽8)⋊D7, C2×C11⋊C5×#64424, C2×C11⋊C5×#64425, …
maximal quotient ofD3×C11⋊C5×C7⋊D7, C2×C3×C11⋊C5×C7⋊D7, C2×C11⋊C5×C3⋊(C7⋊D7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 67);