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C32×C4×C53⋊C13 #37613639

order24804
automorphism?
homologyAbelianization (H1) = C32×C4×C13 · Schur multiplier (H2) = C3

Aliases

direct productC32×C4×C53⋊C13
unambiguous semidirect product(C4×C53)⋊(C32×C13)
unambiguous semidirect product(C3×C4×C53)⋊(C3×C13)
unambiguous semidirect product(C32×C4×C53)⋊C13

Splittings

Fitting, HallC32×C4×C53 ⋊ C13
derived, SylowC53 ⋊ C32×C4×C13
HallC32×C53 ⋊ C4×C13
HallC4×C53 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC32×C4C53⋊C13
commutator, hypocenterC53C32×C4×C13
FrattiniC2C2×C32×C53⋊C13
FittingC32×C4×C53C13
socleC2×C32×C53C2×C13
prime radicalC2×C32×C53⋊C13C2
cosocleC2×C53C2×C32×C13
LCSG ▷ C53
UCSC1 ◁ C32×C4

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1908

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 71);