Finite Group Databasebeta

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C59×C3⋊(Dic13⋊C3) #42120201

order27612
automorphism?
homologyAbelianization (H1) = C3×C4×C59 · Schur multiplier (H2) = C1

Aliases

direct productC59×C3⋊(Dic13⋊C3)
unambiguous semidirect productC3⋊(C59×Dic13⋊C3)
unambiguous semidirect productDic39⋊(C3×C59)
unambiguous semidirect product(C59×Dic39)⋊C3

Splittings

derivedC3×C13 ⋊ C3×C4×C59
HallC3×C13⋊C3×C59 ⋊ C4
HallC13×C59 ⋊ C3×Dic3
HallC3×C13⋊C3 ⋊ C4×C59
SylowC13 ⋊ C3×Dic3×C59

Subgroups

subgroupG/H
center, hypercenterC2×C59C3⋊(D13⋊C3)
commutator, hypocenterC3×C13C3×C4×C59
FrattiniC2C59×C3⋊(D13⋊C3)
Fitting, socleC2×C3×C13×C59C2×C3
prime radicalC2×C3×C13⋊C3×C59C2
cosocleC2×C3×C13C2×C3×C59
LCSG ▷ C3×C13
UCSC1 ◁ C2×C59

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9204

Conjugacy classes & character table

1770 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27612, 45);