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C22×C37×C11⋊C5 #22550784

order8140
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C22×C5×C37 · Schur multiplier (H2) = C2

Aliases

direct productC22×C37×C11⋊C5
unambiguous semidirect product(C22×C11)⋊(C5×C37)
unambiguous semidirect product(C22×C11×C37)⋊C5

Splittings

Fitting, socle, HallC22×C11×C37 ⋊ C5
derived, SylowC11 ⋊ C22×C5×C37
HallC11×C37 ⋊ C22×C5
HallC22×C11 ⋊ C5×C37

Subgroups

subgroupG/H
center, hypercenterC22×C37C11⋊C5
commutator, hypocenterC11C22×C5×C37
FrattiniC1G
Fitting, socleC22×C11×C37C5
LCSG ▷ C11
UCSC1 ◁ C22×C37

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1036 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofA4×C37×C11⋊C5, C11⋊C5×C22⋊(C37⋊C3), C22×C11⋊C5×C37⋊C3, …
maximal normal subgroup ofA4×C37×C11⋊C5, C11⋊C5×C22⋊(C37⋊C3), C22×C11⋊C5×C37⋊C3, …
maximal quotient ofC2×D3×C37×C11⋊C5, C22×C3×C37×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8140, 20);