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C4×C7×C211⋊C3 #31799371

order17724
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×C211⋊C3

Splittings

Fitting, HallC4×C7×C211 ⋊ C3
derived, SylowC211 ⋊ C3×C4×C7
HallC7×C211 ⋊ C3×C4
HallC4×C211 ⋊ C3×C7

Subgroups

subgroupG/H
center, hypercenterC4×C7C211⋊C3
commutator, hypocenterC211C3×C4×C7
FrattiniC2C2×C7×C211⋊C3
FittingC4×C7×C211C3
socleC2×C7×C211C2×C3
prime radicalC2×C7×C211⋊C3C2
cosocleC2×C211C2×C3×C7
LCSG ▷ C211
UCSC1 ◁ C4×C7

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5908

Conjugacy classes & character table

2044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17724, 3);