Finite Group Databasebeta

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C4⋊C4×C13⋊C9 #14272425

order1872
automorphism?
homologyAbelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2

Aliases

direct productC4⋊C4×C13⋊C9
unambiguous semidirect productC4⋊(C4×C13⋊C9)
unambiguous semidirect product(C13×C4⋊C4)⋊C9

Splittings

HallC13×C4⋊C4 ⋊ C9
SylowC13 ⋊ C9×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22×C3C22×C13⋊C3
commutatorC2×C13C2×C4×C9
FittingC3×C13×C4⋊C4C3
socle, prime radical, cosocleC22×C3×C13C22×C3
hypercenterC3×C4⋊C4C13⋊C3
hypocenterC13C9×C4⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1872

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1872, 53);