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C2×#20263756⋊C3 #49185751

order38130
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×#20263756⋊C3
unambiguous semidirect product(C2×#20263756)⋊C3

Splittings

Fitting, socle, HallC2×C31×C41 ⋊ C3×C5
derived, HallC31×C41 ⋊ C2×C3×C5
HallC2×#20263756 ⋊ C3
HallC2×C41×C31⋊C3 ⋊ C5
Hall#20263756 ⋊ C2×C3
HallC41×C31⋊C3 ⋊ C2×C5
HallC2×C31⋊C3 ⋊ C41⋊C5
HallC31⋊C3 ⋊ C2×C41⋊C5
HallC2×C41 ⋊ (C31⋊C3)⋊C5
HallC2×C31 ⋊ C3×C41⋊C5
SylowC41 ⋊ C2×(C31⋊C3)⋊C5
SylowC31 ⋊ C2×C3×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC2#20263756⋊C3
commutator, cosocle, hypocenterC31×C41C2×C3×C5
FrattiniC1G
Fitting, socleC2×C31×C41C3×C5
LCSG ▷ C31×C41
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2542

Conjugacy classes & character table

242 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38130, 14);