Finite Group Databasebeta

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C3×C11×Dic3×C83 #45659646

order32868
automorphism?
homologyAbelianization (H1) = C3×C4×C11×C83 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×Dic3×C83
unambiguous semidirect productC3⋊(C3×C4×C11×C83)

Splittings

derivedC3 ⋊ C3×C4×C11×C83
HallC32×C11×C83 ⋊ C4
HallC32×C83 ⋊ C4×C11
HallC32×C11 ⋊ C4×C83
SylowC32 ⋊ C4×C11×C83

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11×C83D3
commutator, hypocenterC3C3×C4×C11×C83
FrattiniC2C3×D3×C11×C83
Fitting, socle, prime radicalC2×C32×C11×C83C2
cosocleC2×C3C2×C3×C11×C83
LCSG ▷ C3
UCSC1 ◁ C2×C3×C11×C83

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10956

Conjugacy classes & character table

16434 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32868, 33);