Finite Group Databasebeta

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C67×C3⋊(Dic13⋊C3) #44535660

order31356
automorphism?
homologyAbelianization (H1) = C3×C4×C67 · Schur multiplier (H2) = C1

Aliases

direct productC67×C3⋊(Dic13⋊C3)
unambiguous semidirect productC3⋊(C67×Dic13⋊C3)
unambiguous semidirect productDic39⋊(C3×C67)

Splittings

derivedC3×C13 ⋊ C3×C4×C67
HallC3×C13⋊C3×C67 ⋊ C4
HallC13×C67 ⋊ C3×Dic3
HallC3×C13⋊C3 ⋊ C4×C67
SylowC13 ⋊ C3×Dic3×C67

Subgroups

subgroupG/H
center, hypercenterC2×C67C3⋊(D13⋊C3)
commutator, hypocenterC3×C13C3×C4×C67
FrattiniC2C67×C3⋊(D13⋊C3)
Fitting, socleC2×C3×C13×C67C2×C3
prime radicalC2×C3×C13⋊C3×C67C2
cosocleC2×C3×C13C2×C3×C67
LCSG ▷ C3×C13
UCSC1 ◁ C2×C67

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10452

Conjugacy classes & character table

2010 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 96);