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C5×C73×C22⋊ΓL(1,𝔽8) #44501452

order30660
automorphism?
homologyAbelianization (H1) = C3×C5×C73 · Schur multiplier (H2) = C2

Aliases

direct productC5×C73×C22⋊ΓL(1,𝔽8)
unambiguous semidirect productC22⋊(C5×ΓL(1,𝔽8)×C73)
unambiguous semidirect productC7⋊(C5×A4×C73)
unambiguous semidirect product(C22×C5)⋊(ΓL(1,𝔽8)×C73)
unambiguous semidirect product(C5×C7)⋊(A4×C73)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5×C73C22⋊ΓL(1,𝔽8)
commutator, cosocle, hypocenterC22×C7C3×C5×C73
FrattiniC1G
Fitting, socleC22×C5×C7×C73C3
LCSG ▷ C22×C7
UCSC1 ◁ C5×C73

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10220

Conjugacy classes & character table

4380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 215);