Finite Group Databasebeta

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C4×C7×C271⋊C3 #36384607

order22764
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×C271⋊C3
unambiguous semidirect product(C4×C271)⋊(C3×C7)

Splittings

Fitting, HallC4×C7×C271 ⋊ C3
derived, SylowC271 ⋊ C3×C4×C7
HallC7×C271 ⋊ C3×C4
HallC4×C271 ⋊ C3×C7

Subgroups

subgroupG/H
center, hypercenterC4×C7C271⋊C3
commutator, hypocenterC271C3×C4×C7
FrattiniC2C2×C7×C271⋊C3
FittingC4×C7×C271C3
socleC2×C7×C271C2×C3
prime radicalC2×C7×C271⋊C3C2
cosocleC2×C271C2×C3×C7
LCSG ▷ C271
UCSC1 ◁ C4×C7

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7588

Conjugacy classes & character table

2604 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22764, 2);