Finite Group Databasebeta

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C2×C3×D523⋊C3 #34038005

order18828
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×D523⋊C3
unambiguous semidirect productD523⋊(C2×C32)
unambiguous semidirect product(C523⋊C3)⋊(C22×C3)
unambiguous semidirect product(C2×D523)⋊C32
unambiguous semidirect product(C2×C523⋊C3)⋊(C2×C3)
unambiguous semidirect product(C2×C3×D523)⋊C3

Splittings

Fitting, socleC2×C3×C523 ⋊ C2×C3
derived, SylowC523 ⋊ C22×C32
HallC3×C523⋊C3 ⋊ C22
HallC2×D523 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC2×C3D523⋊C3
commutator, cosocle, hypocenterC523C22×C32
FrattiniC1G
Fitting, socleC2×C3×C523C2×C3
LCSG ▷ C523
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3138

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18828, 34);