Finite Group Databasebeta

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C2×C7×C11×C52⋊C3 #26040528

order11550
isoclinismisoclinic class of C52⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C5

Aliases

direct productC2×C7×C11×C52⋊C3
unambiguous semidirect product(C2×C52)⋊(C3×C7×C11)
unambiguous semidirect product(C2×C52×C11)⋊(C3×C7)

Splittings

Fitting, socle, HallC2×C52×C7×C11 ⋊ C3
derived, SylowC52 ⋊ C2×C3×C7×C11
HallC52×C7×C11 ⋊ C2×C3
HallC2×C52×C11 ⋊ C3×C7
HallC2×C52×C7 ⋊ C3×C11
HallC52×C11 ⋊ C2×C3×C7
HallC52×C7 ⋊ C2×C3×C11
HallC2×C52 ⋊ C3×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11C52⋊C3
commutator, cosocle, hypocenterC52C2×C3×C7×C11
FrattiniC1G
Fitting, socleC2×C52×C7×C11C3
LCSG ▷ C52
UCSC1 ◁ C2×C7×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1694 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×C11×#64470, C7×C11⋊#64470, C11×C7⋊#64470, …
maximal normal subgroup ofC7×C11×#64470, C7×C11⋊#64470, C11×C7⋊#64470, …
maximal quotient ofC4×C7×C11×C52⋊C3, C22×C7×C11×C52⋊C3, C2×C7×C11×C52⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 92);