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C2×ΓL(1,𝔽8)×D445 #49153157

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

Aliases

direct productC2×ΓL(1,𝔽8)×D445
unambiguous semidirect product(C2×C5)⋊(ΓL(1,𝔽8)×D89)
unambiguous semidirect product(C2×C89)⋊(D5×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C7×D445)⋊C3

Splittings

Fitting, socleC2×C5×C7×C89 ⋊ C2×C3
derived, HallC5×C7×C89 ⋊ C22×C3
HallC2×C7×D445 ⋊ C3
HallC5×ΓL(1,𝔽8)×C89 ⋊ C22
HallΓL(1,𝔽8)×C89 ⋊ C2×D5
HallC7×C89 ⋊ C2×C3×D5
HallC5×C89 ⋊ C22×ΓL(1,𝔽8)
HallC5×ΓL(1,𝔽8) ⋊ C2×D89
SylowC89 ⋊ C2×D5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×C3×D89
SylowC7 ⋊ C2×C3×D445
SylowC5 ⋊ C2×ΓL(1,𝔽8)×D89

Subgroups

subgroupG/H
center, hypercenterC2ΓL(1,𝔽8)×D445
commutator, cosocle, hypocenterC5×C7×C89C22×C3
FrattiniC1G
Fitting, socleC2×C5×C7×C89C2×C3
LCSG ▷ C5×C7×C89
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6230

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 51);