Finite Group Databasebeta

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C2×C5×C7×C11×D7 #24924800

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

Aliases

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

Splittings

Fitting, socleC2×C5×C72×C11 ⋊ C2
derivedC7 ⋊ C22×C5×C7×C11
HallC5×C72×C11 ⋊ C22
HallC72×C11 ⋊ C22×C5
HallC5×C72 ⋊ C22×C11
SylowC72 ⋊ C22×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7×C11D7
commutator, cosocle, hypocenterC7C22×C5×C7×C11
FrattiniC1G
Fitting, socleC2×C5×C72×C11C2
LCSG ▷ C7
UCSC1 ◁ C2×C5×C7×C11

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3850 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C11×#64418, C2×C5×C7×C11×AGL(1,𝔽7), C2×C5×C11×D7×ΓL(1,𝔽8), …
maximal normal subgroup ofC2×C5×C7×C11×AGL(1,𝔽7), C2×C5×C11×D7×ΓL(1,𝔽8), C2×C5×C11×#64423, …
maximal quotient ofC5×D3×C7×C11×D7, C2×C3×C5×C7×C11×D7, C2×C5×C7×C11×D21

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 113);