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C2×C5×AGL(1,𝔽7)×C79 #45684464

order33180
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C79 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×AGL(1,𝔽7)×C79
unambiguous semidirect productD7⋊(C2×C3×C5×C79)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C5×C79)
unambiguous semidirect product(C2×D7)⋊(C3×C5×C79)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C5×C79)
unambiguous semidirect product(C2×C5×D7)⋊(C3×C79)

Splittings

Fitting, socleC2×C5×C7×C79 ⋊ C2×C3
derived, SylowC7 ⋊ C22×C3×C5×C79
HallC2×C5×D7×C79 ⋊ C3
HallC5×ΓL(1,𝔽8)×C79 ⋊ C22
HallC5×C7×C79 ⋊ C22×C3
HallC2×D7×C79 ⋊ C3×C5
HallΓL(1,𝔽8)×C79 ⋊ C22×C5
HallC7×C79 ⋊ C22×C3×C5
HallC2×C5×D7 ⋊ C3×C79
HallC5×ΓL(1,𝔽8) ⋊ C22×C79
HallC5×C7 ⋊ C22×C3×C79
HallC2×D7 ⋊ C3×C5×C79
HallΓL(1,𝔽8) ⋊ C22×C5×C79

Subgroups

subgroupG/H
center, hypercenterC2×C5×C79AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C22×C3×C5×C79
FrattiniC1G
Fitting, socleC2×C5×C7×C79C2×C3
LCSG ▷ C7
UCSC1 ◁ C2×C5×C79

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5530

Conjugacy classes & character table

5530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33180, 95);