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C4×C13×#10620253 #46799212

order33852
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13×#10620253

Splittings

Fitting, HallC4×C7×C13×C31 ⋊ C3
derived, HallC7×C31 ⋊ C3×C4×C13
HallC7×C13×C31 ⋊ C3×C4
HallC4×C13×C31 ⋊ ΓL(1,𝔽8)
HallC4×C7×C31 ⋊ C3×C13
HallC13×C31 ⋊ C4×ΓL(1,𝔽8)
HallC4×C7×C13 ⋊ C31⋊C3
HallC4×C31 ⋊ C13×ΓL(1,𝔽8)
HallC7×C13 ⋊ C4×C31⋊C3
SylowC31 ⋊ C4×C13×ΓL(1,𝔽8)
HallC4×C7 ⋊ C13×C31⋊C3
SylowC7 ⋊ C4×C13×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC4×C13#10620253
commutator, hypocenterC7×C31C3×C4×C13
FrattiniC2C2×C13×#10620253
FittingC4×C7×C13×C31C3
socleC2×C7×C13×C31C2×C3
prime radicalC2×C13×#10620253C2
cosocleC2×C7×C31C2×C3×C13
LCSG ▷ C7×C31
UCSC1 ◁ C4×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11284

Conjugacy classes & character table

3900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33852, 7);