Finite Group Databasebeta

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C4×C47×C61⋊C3 #46806124

order34404
automorphism?
homologyAbelianization (H1) = C3×C4×C47 · Schur multiplier (H2) = C1

Aliases

direct productC4×C47×C61⋊C3
unambiguous semidirect product(C4×C61)⋊(C3×C47)
unambiguous semidirect product(C4×C47×C61)⋊C3

Splittings

Fitting, HallC4×C47×C61 ⋊ C3
derived, SylowC61 ⋊ C3×C4×C47
HallC47×C61 ⋊ C3×C4
HallC4×C61 ⋊ C3×C47

Subgroups

subgroupG/H
center, hypercenterC4×C47C61⋊C3
commutator, hypocenterC61C3×C4×C47
FrattiniC2C2×C47×C61⋊C3
FittingC4×C47×C61C3
socleC2×C47×C61C2×C3
prime radicalC2×C47×C61⋊C3C2
cosocleC2×C61C2×C3×C47
LCSG ▷ C61
UCSC1 ◁ C4×C47

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11468

Conjugacy classes & character table

4324 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34404, 2);