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C2×C5×AGL(1,𝔽7)×C89 #49153151

order37380
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C89 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×AGL(1,𝔽7)×C89
unambiguous semidirect productD7⋊(C2×C3×C5×C89)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C5×C89)
unambiguous semidirect product(C2×D7)⋊(C3×C5×C89)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C5×C89)
unambiguous semidirect product(C2×C5×D7)⋊(C3×C89)
unambiguous semidirect product(C2×D7×C89)⋊(C3×C5)
unambiguous semidirect product(C2×C5×D7×C89)⋊C3

Splittings

Fitting, socleC2×C5×C7×C89 ⋊ C2×C3
derived, SylowC7 ⋊ C22×C3×C5×C89
HallC2×C5×D7×C89 ⋊ C3
HallC5×ΓL(1,𝔽8)×C89 ⋊ C22
HallC5×C7×C89 ⋊ C22×C3
HallC2×D7×C89 ⋊ C3×C5
HallΓL(1,𝔽8)×C89 ⋊ C22×C5
HallC7×C89 ⋊ C22×C3×C5
HallC2×C5×D7 ⋊ C3×C89
HallC5×ΓL(1,𝔽8) ⋊ C22×C89
HallC5×C7 ⋊ C22×C3×C89
HallC2×D7 ⋊ C3×C5×C89
HallΓL(1,𝔽8) ⋊ C22×C5×C89

Subgroups

subgroupG/H
center, hypercenterC2×C5×C89AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C22×C3×C5×C89
FrattiniC1G
Fitting, socleC2×C5×C7×C89C2×C3
LCSG ▷ C7
UCSC1 ◁ C2×C5×C89

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6230

Conjugacy classes & character table

6230 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 45);