Finite Group Databasebeta

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C2×C5×C11×C7⋊D7 #24924798

order10780
isoclinismisoclinic class of C7⋊D7
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2×C7

Aliases

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

Splittings

Fitting, socleC2×C5×C72×C11 ⋊ C2
derived, SylowC72 ⋊ C22×C5×C11
HallC5×C72×C11 ⋊ C22
HallC72×C11 ⋊ C22×C5
HallC5×C72 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11C7⋊D7
commutator, cosocle, hypocenterC72C22×C5×C11
FrattiniC1G
Fitting, socleC2×C5×C72×C11C2
LCSG ▷ C72
UCSC1 ◁ C2×C5×C11

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2860 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C11×ΓL(1,𝔽8)⋊D7, C2×C5×C11×#64424, C2×C5×C11×#64425, …
maximal normal subgroup ofC2×C5×C11×ΓL(1,𝔽8)⋊D7, C2×C5×C11×#64424, C2×C5×C11×#64425, …
maximal quotient ofC5×D3×C11×C7⋊D7, C2×C3×C5×C11×C7⋊D7, C2×C5×C11×C3⋊(C7⋊D7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 111);