Finite Group Databasebeta

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C2×C3×C13⋊C3×D53 #37613700

order24804
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C13⋊C3×D53
unambiguous semidirect productC53⋊(C22×C3×C13⋊C3)
unambiguous semidirect product(C2×C53)⋊(C2×C3×C13⋊C3)
unambiguous semidirect product(C2×C13×D53)⋊C32
unambiguous semidirect product(C2×C3×C13×D53)⋊C3

Splittings

Fitting, socleC2×C3×C13×C53 ⋊ C2×C3
derived, HallC13×C53 ⋊ C22×C32
HallC3×C13⋊C3×C53 ⋊ C22
HallC2×C13×D53 ⋊ C32
SylowC53 ⋊ C22×C3×C13⋊C3
SylowC13 ⋊ C2×C32×D53

Subgroups

subgroupG/H
center, hypercenterC2×C3C13⋊C3×D53
commutator, cosocle, hypocenterC13×C53C22×C32
FrattiniC1G
Fitting, socleC2×C3×C13×C53C2×C3
LCSG ▷ C13×C53
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4134

Conjugacy classes & character table

1176 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 132);