Finite Group Databasebeta

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C4×C7×C241⋊C3 #35202256

order20244
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×C241⋊C3
unambiguous semidirect product(C4×C241)⋊(C3×C7)

Splittings

Fitting, HallC4×C7×C241 ⋊ C3
derived, SylowC241 ⋊ C3×C4×C7
HallC7×C241 ⋊ C3×C4
HallC4×C241 ⋊ C3×C7

Subgroups

subgroupG/H
center, hypercenterC4×C7C241⋊C3
commutator, hypocenterC241C3×C4×C7
FrattiniC2C2×C7×C241⋊C3
FittingC4×C7×C241C3
socleC2×C7×C241C2×C3
prime radicalC2×C7×C241⋊C3C2
cosocleC2×C241C2×C3×C7
LCSG ▷ C241
UCSC1 ◁ C4×C7

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6748

Conjugacy classes & character table

2324 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20244, 2);