Finite Group Databasebeta

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C2×C3×C5×C229⋊C3 #35207302

order20610
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C5×C229⋊C3
unambiguous semidirect product(C2×C229)⋊(C32×C5)
unambiguous semidirect product(C2×C3×C229)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C229)⋊C32
unambiguous semidirect product(C2×C3×C5×C229)⋊C3

Splittings

Fitting, socleC2×C3×C5×C229 ⋊ C3
derived, SylowC229 ⋊ C2×C32×C5
HallC2×C5×C229 ⋊ C32
HallC5×C229 ⋊ C2×C32
HallC2×C229 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C229⋊C3
commutator, cosocle, hypocenterC229C2×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C229C3
LCSG ▷ C229
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6870

Conjugacy classes & character table

2370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20610, 21);