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C5×C22⋊#13095275 #44501453

order30660
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×C22⋊#13095275
unambiguous semidirect productC22⋊(C5×#13095275)
unambiguous semidirect product(C22×C5)⋊#13095275

Splittings

Fitting, socle, HallC22×C5×C7×C73 ⋊ C3
derived, HallC22×C7×C73 ⋊ C3×C5
HallC5×C7×C73 ⋊ A4
HallC22×C5×C73 ⋊ ΓL(1,𝔽8)
HallC7×C73 ⋊ C5×A4
HallC5×C73 ⋊ C22⋊ΓL(1,𝔽8)
HallC22×C73 ⋊ C5×ΓL(1,𝔽8)
HallC22×C5×C7 ⋊ C73⋊C3
SylowC73 ⋊ C5×C22⋊ΓL(1,𝔽8)
HallC5×C7 ⋊ C22⋊(C73⋊C3)
HallC22×C7 ⋊ C5×C73⋊C3
HallC22×C5 ⋊ #13095275
SylowC7 ⋊ C5×C22⋊(C73⋊C3)
SylowC22 ⋊ C5×#13095275

Subgroups

subgroupG/H
center, hypercenterC5C22⋊#13095275
commutator, cosocle, hypocenterC22×C7×C73C3×C5
FrattiniC1G
Fitting, socleC22×C5×C7×C73C3
LCSG ▷ C22×C7×C73
UCSC1 ◁ C5

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10220

Conjugacy classes & character table

3420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 216);