Finite Group Databasebeta

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C4×C13⋊C3×C167 #39907513

order26052
automorphism?
homologyAbelianization (H1) = C3×C4×C167 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13⋊C3×C167
unambiguous semidirect product(C4×C13)⋊(C3×C167)
unambiguous semidirect product(C4×C13×C167)⋊C3

Splittings

Fitting, HallC4×C13×C167 ⋊ C3
derived, SylowC13 ⋊ C3×C4×C167
HallC13×C167 ⋊ C3×C4
HallC4×C13 ⋊ C3×C167

Subgroups

subgroupG/H
center, hypercenterC4×C167C13⋊C3
commutator, hypocenterC13C3×C4×C167
FrattiniC2C2×C13⋊C3×C167
FittingC4×C13×C167C3
socleC2×C13×C167C2×C3
prime radicalC2×C13⋊C3×C167C2
cosocleC2×C13C2×C3×C167
LCSG ▷ C13
UCSC1 ◁ C4×C167

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8684

Conjugacy classes & character table

4676 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26052, 2);