Finite Group Databasebeta

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C2×C32×D53⋊C13 #37613672

order24804
automorphism?
homologyAbelianization (H1) = C22×C32×C13 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×D53⋊C13
unambiguous semidirect productD53⋊(C2×C32×C13)
unambiguous semidirect product(C2×D53)⋊(C32×C13)
unambiguous semidirect product(C2×C3×D53)⋊(C3×C13)
unambiguous semidirect product(C53⋊C13)⋊(C22×C32)
unambiguous semidirect product(C2×C53⋊C13)⋊(C2×C32)
unambiguous semidirect product(C2×C32×D53)⋊C13

Splittings

Fitting, socleC2×C32×C53 ⋊ C2×C13
derived, SylowC53 ⋊ C22×C32×C13
HallC32×C53⋊C13 ⋊ C22
HallC2×C32×D53 ⋊ C13
HallC53⋊C13 ⋊ C22×C32
HallC32×C53 ⋊ C22×C13
HallC2×D53 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC2×C32D53⋊C13
commutator, cosocle, hypocenterC53C22×C32×C13
FrattiniC1G
Fitting, socleC2×C32×C53C2×C13
LCSG ▷ C53
UCSC1 ◁ C2×C32

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 954

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 104);