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C2×C32×#13133723 #44501865

order30690
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C32×#13133723

Splittings

Fitting, socle, HallC2×C32×C11×C31 ⋊ C5
derived, HallC11×C31 ⋊ C2×C32×C5
HallC32×C11×C31 ⋊ C2×C5
HallC2×C11×C31 ⋊ C32×C5
HallC2×C32×C31 ⋊ C11⋊C5
HallC32×C31 ⋊ C2×C11⋊C5
HallC2×C32×C11 ⋊ ΓL(1,𝔽32)
HallC32×C11 ⋊ C2×ΓL(1,𝔽32)
HallC2×C31 ⋊ C32×C11⋊C5
SylowC31 ⋊ C2×C32×C11⋊C5
HallC2×C11 ⋊ C32×ΓL(1,𝔽32)
SylowC11 ⋊ C2×C32×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC2×C32#13133723
commutator, cosocle, hypocenterC11×C31C2×C32×C5
FrattiniC1G
Fitting, socleC2×C32×C11×C31C5
LCSG ▷ C11×C31
UCSC1 ◁ C2×C32

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6138

Conjugacy classes & character table

1314 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 232);