Finite Group Databasebeta

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C4×C7×C409⋊C3 #46805253

order34356
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×C409⋊C3
unambiguous semidirect product(C4×C409)⋊(C3×C7)

Splittings

Fitting, HallC4×C7×C409 ⋊ C3
derived, SylowC409 ⋊ C3×C4×C7
HallC7×C409 ⋊ C3×C4
HallC4×C409 ⋊ C3×C7

Subgroups

subgroupG/H
center, hypercenterC4×C7C409⋊C3
commutator, hypocenterC409C3×C4×C7
FrattiniC2C2×C7×C409⋊C3
FittingC4×C7×C409C3
socleC2×C7×C409C2×C3
prime radicalC2×C7×C409⋊C3C2
cosocleC2×C409C2×C3×C7
LCSG ▷ C409
UCSC1 ◁ C4×C7

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11452

Conjugacy classes & character table

3892 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34356, 2);