Finite Group Databasebeta

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C2×C5×D21×C89 #49153229

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

Aliases

direct productC2×C5×D21×C89
unambiguous semidirect product(C2×C3)⋊(C5×D7×C89)
unambiguous semidirect product(C2×C7)⋊(C5×D3×C89)

Splittings

Fitting, socleC2×C3×C5×C7×C89 ⋊ C2
derived, HallC3×C7 ⋊ C22×C5×C89
HallC3×C5×C7×C89 ⋊ C22
HallC5×C7×C89 ⋊ C2×D3
HallC3×C7×C89 ⋊ C22×C5
HallC3×C5×C89 ⋊ C2×D7
HallC7×C89 ⋊ C2×C5×D3
HallC3×C89 ⋊ C2×C5×D7
HallC3×C5×C7 ⋊ C22×C89
HallC5×C7 ⋊ C2×D3×C89
HallC3×C5 ⋊ C2×D7×C89
SylowC7 ⋊ C2×C5×D3×C89
SylowC3 ⋊ C2×C5×D7×C89

Subgroups

subgroupG/H
center, hypercenterC2×C5×C89D21
commutator, cosocle, hypocenterC3×C7C22×C5×C89
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C89C2
LCSG ▷ C3×C7
UCSC1 ◁ C2×C5×C89

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18690

Conjugacy classes & character table

10680 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 123);