Finite Group Databasebeta

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C2×C5×D1605 #44545714

order32100
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D1605
unambiguous semidirect product(C2×C3)⋊(C5×D535)
unambiguous semidirect product(C2×C5)⋊(C5×D321)
unambiguous semidirect product(C2×C107)⋊(C5×D15)

Splittings

Fitting, socleC2×C3×C52×C107 ⋊ C2
derivedC3×C5×C107 ⋊ C22×C5
HallC3×C52×C107 ⋊ C22
HallC52×C107 ⋊ C2×D3
HallC3×C107 ⋊ C2×C5×D5
SylowC107 ⋊ C2×C5×D15
HallC3×C52 ⋊ C2×D107
SylowC52 ⋊ C2×D321
SylowC3 ⋊ C2×C5×D535

Subgroups

subgroupG/H
center, hypercenterC2×C5D1605
commutator, cosocle, hypocenterC3×C5×C107C22×C5
FrattiniC1G
Fitting, socleC2×C3×C52×C107C2
LCSG ▷ C3×C5×C107
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6420

Conjugacy classes & character table

8040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32100, 112);