Finite Group Databasebeta

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C3×C53×Dic13⋊C3 #37613640

order24804
automorphism?
homologyAbelianization (H1) = C32×C4×C53 · Schur multiplier (H2) = C3

Aliases

direct productC3×C53×Dic13⋊C3
unambiguous semidirect productDic13⋊(C32×C53)
unambiguous semidirect product(C3×Dic13)⋊(C3×C53)
unambiguous semidirect product(Dic13×C53)⋊C32
unambiguous semidirect product(C3×Dic13×C53)⋊C3

Splittings

derived, SylowC13 ⋊ C32×C4×C53
HallC3×C13⋊C3×C53 ⋊ C4
HallDic13×C53 ⋊ C32
HallC13×C53 ⋊ C32×C4
HallC3×C13⋊C3 ⋊ C4×C53
HallDic13 ⋊ C32×C53

Subgroups

subgroupG/H
center, hypercenterC2×C3×C53D13⋊C3
commutator, hypocenterC13C32×C4×C53
FrattiniC2C3×C53×D13⋊C3
Fitting, socleC2×C3×C13×C53C2×C3
prime radicalC2×C3×C13⋊C3×C53C2
cosocleC2×C13C2×C32×C53
LCSG ▷ C13
UCSC1 ◁ C2×C3×C53

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8268

Conjugacy classes & character table

2544 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 72);