Finite Group Databasebeta

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C2×C32×C11×ΓL(1,𝔽32) #44501860

order30690
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C11 · Schur multiplier (H2) = C3

Aliases

direct productC2×C32×C11×ΓL(1,𝔽32)
unambiguous semidirect product(C2×C32×C31)⋊(C5×C11)

Splittings

Fitting, socle, HallC2×C32×C11×C31 ⋊ C5
derived, SylowC31 ⋊ C2×C32×C5×C11
HallC32×C11×C31 ⋊ C2×C5
HallC2×C11×C31 ⋊ C32×C5
HallC2×C32×C31 ⋊ C5×C11
HallC11×C31 ⋊ C2×C32×C5
HallC32×C31 ⋊ C2×C5×C11
HallC2×C31 ⋊ C32×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C32×C11ΓL(1,𝔽32)
commutator, cosocle, hypocenterC31C2×C32×C5×C11
FrattiniC1G
Fitting, socleC2×C32×C11×C31C5
LCSG ▷ C31
UCSC1 ◁ C2×C32×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6138

Conjugacy classes & character table

2178 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 227);