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C53×C3⋊(Dic13⋊C3) #37613643

order24804
automorphism?
homologyAbelianization (H1) = C3×C4×C53 · Schur multiplier (H2) = C1

Aliases

direct productC53×C3⋊(Dic13⋊C3)
unambiguous semidirect productC3⋊(C53×Dic13⋊C3)
unambiguous semidirect productDic39⋊(C3×C53)
unambiguous semidirect product(C53×Dic39)⋊C3

Splittings

derivedC3×C13 ⋊ C3×C4×C53
HallC3×C13⋊C3×C53 ⋊ C4
HallC13×C53 ⋊ C3×Dic3
HallC3×C13⋊C3 ⋊ C4×C53
SylowC13 ⋊ C3×Dic3×C53

Subgroups

subgroupG/H
center, hypercenterC2×C53C3⋊(D13⋊C3)
commutator, hypocenterC3×C13C3×C4×C53
FrattiniC2C53×C3⋊(D13⋊C3)
Fitting, socleC2×C3×C13×C53C2×C3
prime radicalC2×C3×C13⋊C3×C53C2
cosocleC2×C3×C13C2×C3×C53
LCSG ▷ C3×C13
UCSC1 ◁ C2×C53

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8268

Conjugacy classes & character table

1590 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 75);