Finite Group Databasebeta

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C2×C3⋊D2805 #46778216

order33660
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3⋊D2805
unambiguous semidirect product(C2×C3)⋊D2805
unambiguous semidirect product(C2×C5)⋊(C3⋊D561)
unambiguous semidirect product(C2×C11)⋊(C3⋊D255)
unambiguous semidirect product(C2×C17)⋊(C3⋊D165)

Splittings

Fitting, socleC2×C32×C5×C11×C17 ⋊ C2
derived, HallC32×C5×C11×C17 ⋊ C22
HallC32×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C2×C3⋊D3
HallC32×C5×C17 ⋊ C2×D11
HallC32×C5×C11 ⋊ C2×D17
HallC11×C17 ⋊ C2×C3⋊D15
HallC32×C17 ⋊ C2×D55
HallC32×C11 ⋊ C2×D85
HallC5×C17 ⋊ C2×C3⋊D33
HallC5×C11 ⋊ C2×C3⋊D51
HallC32×C5 ⋊ C2×D187
SylowC17 ⋊ C2×C3⋊D165
SylowC11 ⋊ C2×C3⋊D255
SylowC32 ⋊ C2×D935
SylowC5 ⋊ C2×C3⋊D561

Subgroups

subgroupG/H
center, hypercenterC2C3⋊D2805
commutator, cosocle, hypocenterC32×C5×C11×C17C22
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C17C2
LCSG ▷ C32×C5×C11×C17
UCSC1 ◁ C2

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16830

Conjugacy classes & character table

8418 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 384);