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C4×C7×#10620323 #32913772

order18396
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×#10620323

Splittings

Fitting, HallC4×C7×C73 ⋊ C9
derived, SylowC73 ⋊ C4×C7×C9
HallC7×C73 ⋊ C4×C9
HallC4×C73 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC4×C7#10620323
commutator, hypocenterC73C4×C7×C9
FrattiniC2C2×C7×#10620323
FittingC4×C7×C73C9
socleC2×C7×C73C2×C9
prime radicalC2×C7×C73⋊C3C2×C3
cosocleC2×C73⋊C3C2×C3×C7
LCSG ▷ C73
UCSC1 ◁ C4×C7

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2044

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18396, 90);