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C2×C89×C5⋊AGL(1,𝔽7) #49153154

order37380
automorphism?
homologyAbelianization (H1) = C22×C3×C89 · Schur multiplier (H2) = C2

Aliases

direct productC2×C89×C5⋊AGL(1,𝔽7)
unambiguous semidirect product(C2×C5)⋊(AGL(1,𝔽7)×C89)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(D5×C89)
unambiguous semidirect product(C2×D35)⋊(C3×C89)
unambiguous semidirect product(C2×D35×C89)⋊C3

Splittings

Fitting, socleC2×C5×C7×C89 ⋊ C2×C3
derived, HallC5×C7 ⋊ C22×C3×C89
HallC2×D35×C89 ⋊ C3
HallC5×ΓL(1,𝔽8)×C89 ⋊ C22
HallC5×C7×C89 ⋊ C22×C3
HallΓL(1,𝔽8)×C89 ⋊ C2×D5
HallC7×C89 ⋊ C2×C3×D5
HallC5×C89 ⋊ C2×AGL(1,𝔽7)
HallC2×D35 ⋊ C3×C89
HallC5×ΓL(1,𝔽8) ⋊ C22×C89
HallΓL(1,𝔽8) ⋊ C2×D5×C89
SylowC7 ⋊ C2×C3×D5×C89
SylowC5 ⋊ C2×AGL(1,𝔽7)×C89

Subgroups

subgroupG/H
center, hypercenterC2×C89C5⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7C22×C3×C89
FrattiniC1G
Fitting, socleC2×C5×C7×C89C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C2×C89

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6230

Conjugacy classes & character table

3026 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 48);