Finite Group Databasebeta

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C2×C23×D61⋊C3 #30682803

order16836
isoclinismisoclinic class of D61⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×C23×D61⋊C3
unambiguous semidirect productD61⋊(C2×C3×C23)
unambiguous semidirect product(C61⋊C3)⋊(C22×C23)
unambiguous semidirect product(C2×D61)⋊(C3×C23)
unambiguous semidirect product(C2×C61⋊C3)⋊(C2×C23)
unambiguous semidirect product(C2×C23×D61)⋊C3

Splittings

Fitting, socleC2×C23×C61 ⋊ C2×C3
derived, SylowC61 ⋊ C22×C3×C23
HallC2×C23×D61 ⋊ C3
HallC23×C61⋊C3 ⋊ C22
HallC23×C61 ⋊ C22×C3
HallC2×D61 ⋊ C3×C23
HallC61⋊C3 ⋊ C22×C23

Subgroups

subgroupG/H
center, hypercenterC2×C23D61⋊C3
commutator, cosocle, hypocenterC61C22×C3×C23
FrattiniC1G
Fitting, socleC2×C23×C61C2×C3
LCSG ▷ C61
UCSC1 ◁ C2×C23

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2806

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16836, 17);