Finite Group Databasebeta

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C2×C3×#11925881⋊C5 #49136594

order36270
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×#11925881⋊C5
unambiguous semidirect product(C2×C3×#11925881)⋊C5

Splittings

Fitting, socleC2×C3×C13×C31 ⋊ C3×C5
derived, HallC13×C31 ⋊ C2×C32×C5
HallC2×C3×#11925881 ⋊ C5
HallC2×C13×ΓL(1,𝔽32) ⋊ C32
HallC3×#11925881 ⋊ C2×C5
HallC13×ΓL(1,𝔽32) ⋊ C2×C32
HallC2×C13×C31 ⋊ C32×C5
HallC2×ΓL(1,𝔽32) ⋊ C3×C13⋊C3
HallΓL(1,𝔽32) ⋊ C2×C3×C13⋊C3
HallC2×C31 ⋊ C3×C5×C13⋊C3
SylowC31 ⋊ C2×C3×C5×C13⋊C3
HallC2×C13 ⋊ C3×(C31⋊C3)⋊C5
SylowC13 ⋊ C2×C3×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3#11925881⋊C5
commutator, cosocle, hypocenterC13×C31C2×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C13×C31C3×C5
LCSG ▷ C13×C31
UCSC1 ◁ C2×C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2418

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36270, 114);