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C5×C22⋊#13064104 #43244992

order28140
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×C22⋊#13064104
unambiguous semidirect productC22⋊(C5×#13064104)
unambiguous semidirect product(C22×C5)⋊#13064104

Splittings

Fitting, socle, HallC22×C5×C7×C67 ⋊ C3
derived, HallC22×C7×C67 ⋊ C3×C5
HallC5×C7×C67 ⋊ A4
HallC22×C5×C67 ⋊ ΓL(1,𝔽8)
HallC7×C67 ⋊ C5×A4
HallC5×C67 ⋊ C22⋊ΓL(1,𝔽8)
HallC22×C67 ⋊ C5×ΓL(1,𝔽8)
HallC22×C5×C7 ⋊ C67⋊C3
SylowC67 ⋊ C5×C22⋊ΓL(1,𝔽8)
HallC5×C7 ⋊ C22⋊(C67⋊C3)
HallC22×C7 ⋊ C5×C67⋊C3
HallC22×C5 ⋊ #13064104
SylowC7 ⋊ C5×C22⋊(C67⋊C3)
SylowC22 ⋊ C5×#13064104

Subgroups

subgroupG/H
center, hypercenterC5C22⋊#13064104
commutator, cosocle, hypocenterC22×C7×C67C3×C5
FrattiniC1G
Fitting, socleC22×C5×C7×C67C3
LCSG ▷ C22×C7×C67
UCSC1 ◁ C5

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9380

Conjugacy classes & character table

3140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28140, 168);