Finite Group Databasebeta

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C3×Dic3×C13×C67 #44535685

order31356
automorphism?
homologyAbelianization (H1) = C3×C4×C13×C67 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic3×C13×C67
unambiguous semidirect productC3⋊(C3×C4×C13×C67)

Splittings

derivedC3 ⋊ C3×C4×C13×C67
HallC32×C13×C67 ⋊ C4
HallC32×C67 ⋊ C4×C13
HallC32×C13 ⋊ C4×C67
SylowC32 ⋊ C4×C13×C67

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13×C67D3
commutator, hypocenterC3C3×C4×C13×C67
FrattiniC2C3×D3×C13×C67
Fitting, socle, prime radicalC2×C32×C13×C67C2
cosocleC2×C3C2×C3×C13×C67
LCSG ▷ C3
UCSC1 ◁ C2×C3×C13×C67

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10452

Conjugacy classes & character table

15678 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 121);