Finite Group Databasebeta

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C2×C83×D105 #46852915

order34860
automorphism?
homologyAbelianization (H1) = C22×C83 · Schur multiplier (H2) = C2

Aliases

direct productC2×C83×D105
unambiguous semidirect product(C2×C3)⋊(D35×C83)
unambiguous semidirect product(C2×C5)⋊(D21×C83)
unambiguous semidirect product(C2×C7)⋊(D15×C83)

Splittings

Fitting, socleC2×C3×C5×C7×C83 ⋊ C2
derived, HallC3×C5×C7 ⋊ C22×C83
HallC3×C5×C7×C83 ⋊ C22
HallC5×C7×C83 ⋊ C2×D3
HallC3×C7×C83 ⋊ C2×D5
HallC3×C5×C83 ⋊ C2×D7
HallC7×C83 ⋊ C2×D15
HallC5×C83 ⋊ C2×D21
HallC3×C83 ⋊ C2×D35
HallC5×C7 ⋊ C2×D3×C83
HallC3×C7 ⋊ C2×D5×C83
HallC3×C5 ⋊ C2×D7×C83
SylowC7 ⋊ C2×D15×C83
SylowC5 ⋊ C2×D21×C83
SylowC3 ⋊ C2×D35×C83

Subgroups

subgroupG/H
center, hypercenterC2×C83D105
commutator, cosocle, hypocenterC3×C5×C7C22×C83
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C83C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C2×C83

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17430

Conjugacy classes & character table

8964 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34860, 103);