Finite Group Databasebeta

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C2×C3⋊D3003 #49115031

order36036
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3⋊D3003
unambiguous semidirect product(C2×C3)⋊D3003
unambiguous semidirect product(C2×C7)⋊(C3⋊D429)
unambiguous semidirect product(C2×C11)⋊(C3⋊D273)
unambiguous semidirect product(C2×C13)⋊(C3⋊D231)

Splittings

Fitting, socleC2×C32×C7×C11×C13 ⋊ C2
derived, HallC32×C7×C11×C13 ⋊ C22
HallC32×C11×C13 ⋊ C2×D7
HallC7×C11×C13 ⋊ C2×C3⋊D3
HallC32×C7×C13 ⋊ C2×D11
HallC32×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C3⋊D21
HallC32×C13 ⋊ C2×D77
HallC32×C11 ⋊ C2×D91
HallC7×C13 ⋊ C2×C3⋊D33
HallC7×C11 ⋊ C2×C3⋊D39
HallC32×C7 ⋊ C2×D143
SylowC13 ⋊ C2×C3⋊D231
SylowC11 ⋊ C2×C3⋊D273
SylowC32 ⋊ C2×D1001
SylowC7 ⋊ C2×C3⋊D429

Subgroups

subgroupG/H
center, hypercenterC2C3⋊D3003
commutator, cosocle, hypocenterC32×C7×C11×C13C22
FrattiniC1G
Fitting, socleC2×C32×C7×C11×C13C2
LCSG ▷ C32×C7×C11×C13
UCSC1 ◁ C2

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18018

Conjugacy classes & character table

9012 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 699);