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C5×C22⋊#92788 #23778599

order10140
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×C22⋊#92788
unambiguous semidirect productC22⋊(C5×#92788)
unambiguous semidirect product(C22×C5)⋊#92788

Splittings

Fitting, socle, HallC22×C5×C132 ⋊ C3
derived, HallC22×C132 ⋊ C3×C5
HallC5×C132 ⋊ A4
SylowC132 ⋊ C5×A4
HallC22×C5 ⋊ #92788
SylowC22 ⋊ C5×#92788

Subgroups

subgroupG/H
center, hypercenterC5C22⋊#92788
commutator, cosocle, hypocenterC22×C132C3×C5
FrattiniC1G
Fitting, socleC22×C5×C132C3
LCSG ▷ C22×C132
UCSC1 ◁ C5

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1140 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C13⋊C3×C22⋊(C13⋊C3), C5×#92789⋊A4, C5×A4×#92788, …
maximal normal subgroup ofC5×C13⋊C3×C22⋊(C13⋊C3), C5×#92789⋊A4, C5×A4×#92788, …
maximal quotient ofC5×C22⋊#13095200, C3×C5×C22⋊#92788

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 257);