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C4×C31×ΓL(1,𝔽32) #34063571

order19220
automorphism?
homologyAbelianization (H1) = C4×C5×C31 · Schur multiplier (H2) = C1

Aliases

direct productC4×C31×ΓL(1,𝔽32)
unambiguous semidirect product(C4×C31)⋊(C5×C31)

Splittings

Fitting, HallC4×C312 ⋊ C5
derivedC31 ⋊ C4×C5×C31
SylowC312 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC4×C31ΓL(1,𝔽32)
commutator, hypocenterC31C4×C5×C31
FrattiniC2C2×C31×ΓL(1,𝔽32)
FittingC4×C312C5
socleC2×C312C2×C5
prime radicalC2×C31×ΓL(1,𝔽32)C2
cosocleC2×C31C2×C5×C31
LCSG ▷ C31
UCSC1 ◁ C4×C31

42 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 620

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19220, 28);