Finite Group Databasebeta

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C3×C4×C13×C61⋊C3 #43269751

order28548
automorphism?
homologyAbelianization (H1) = C32×C4×C13 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C13×C61⋊C3
unambiguous semidirect product(C4×C61)⋊(C32×C13)
unambiguous semidirect product(C3×C4×C61)⋊(C3×C13)

Splittings

FittingC3×C4×C13×C61 ⋊ C3
derived, SylowC61 ⋊ C32×C4×C13
HallC4×C13×C61 ⋊ C32
HallC13×C61 ⋊ C32×C4
HallC4×C61 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC3×C4×C13C61⋊C3
commutator, hypocenterC61C32×C4×C13
FrattiniC2C2×C3×C13×C61⋊C3
FittingC3×C4×C13×C61C3
socleC2×C3×C13×C61C2×C3
prime radicalC2×C3×C13×C61⋊C3C2
cosocleC2×C61C2×C32×C13
LCSG ▷ C61
UCSC1 ◁ C3×C4×C13

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9516

Conjugacy classes & character table

3588 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28548, 137);