Finite Group Databasebeta

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C3×C11×Dic3×C79 #44530886

order31284
automorphism?
homologyAbelianization (H1) = C3×C4×C11×C79 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×Dic3×C79
unambiguous semidirect productC3⋊(C3×C4×C11×C79)

Splittings

derivedC3 ⋊ C3×C4×C11×C79
HallC32×C11×C79 ⋊ C4
HallC32×C79 ⋊ C4×C11
HallC32×C11 ⋊ C4×C79
SylowC32 ⋊ C4×C11×C79

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11×C79D3
commutator, hypocenterC3C3×C4×C11×C79
FrattiniC2C3×D3×C11×C79
Fitting, socle, prime radicalC2×C32×C11×C79C2
cosocleC2×C3C2×C3×C11×C79
LCSG ▷ C3
UCSC1 ◁ C2×C3×C11×C79

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10428

Conjugacy classes & character table

15642 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31284, 51);