Finite Group Databasebeta

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C3×C4×C211⋊C7 #31799370

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

Aliases

direct productC3×C4×C211⋊C7
unambiguous semidirect product(C3×C4×C211)⋊C7

Splittings

Fitting, HallC3×C4×C211 ⋊ C7
derived, SylowC211 ⋊ C3×C4×C7
HallC4×C211 ⋊ C3×C7
HallC3×C211 ⋊ C4×C7

Subgroups

subgroupG/H
center, hypercenterC3×C4C211⋊C7
commutator, hypocenterC211C3×C4×C7
FrattiniC2C2×C3×C211⋊C7
FittingC3×C4×C211C7
socleC2×C3×C211C2×C7
prime radicalC2×C3×C211⋊C7C2
cosocleC2×C211C2×C3×C7
LCSG ▷ C211
UCSC1 ◁ C3×C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2532

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17724, 2);