Finite Group Databasebeta

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C4×C7×C223⋊C3 #34035416

order18732
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×C223⋊C3
unambiguous semidirect product(C4×C223)⋊(C3×C7)

Splittings

Fitting, HallC4×C7×C223 ⋊ C3
derived, SylowC223 ⋊ C3×C4×C7
HallC7×C223 ⋊ C3×C4
HallC4×C223 ⋊ C3×C7

Subgroups

subgroupG/H
center, hypercenterC4×C7C223⋊C3
commutator, hypocenterC223C3×C4×C7
FrattiniC2C2×C7×C223⋊C3
FittingC4×C7×C223C3
socleC2×C7×C223C2×C3
prime radicalC2×C7×C223⋊C3C2
cosocleC2×C223C2×C3×C7
LCSG ▷ C223
UCSC1 ◁ C4×C7

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6244

Conjugacy classes & character table

2156 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18732, 2);