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C2×C52×C11×D7 #21440461

order7700
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C22×C52×C11 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C52×C11×D7
unambiguous semidirect productC7⋊(C22×C52×C11)
unambiguous semidirect product(C2×C7)⋊(C2×C52×C11)

Splittings

Fitting, socleC2×C52×C7×C11 ⋊ C2
derived, SylowC7 ⋊ C22×C52×C11
HallC52×C7×C11 ⋊ C22
HallC52×C7 ⋊ C22×C11
HallC7×C11 ⋊ C22×C52

Subgroups

subgroupG/H
center, hypercenterC2×C52×C11D7
commutator, hypocenterC7C22×C52×C11
FrattiniC1G
Fitting, socleC2×C52×C7×C11C2
LCSG ▷ C7
UCSC1 ◁ C2×C52×C11

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2750 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11×D7⋊(C52⋊C3), C2×C11×D7×C52⋊C3, C2×C52×C11×AGL(1,𝔽7), …
maximal normal subgroup ofC2×C11×D7⋊(C52⋊C3), C2×C11×D7×C52⋊C3, C2×C52×C11×AGL(1,𝔽7), …
maximal quotient ofC52×D3×C11×D7, C2×C3×C52×C11×D7, C2×C52×C11×D21

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7700, 125);