Finite Group Databasebeta

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C3×Dic3×C53⋊C13 #37613636

order24804
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic3×C53⋊C13
unambiguous semidirect productC3⋊(C3×C4×C53⋊C13)
unambiguous semidirect product(Dic3×C53)⋊(C3×C13)
unambiguous semidirect product(C3×Dic3×C53)⋊C13

Splittings

derivedC3×C53 ⋊ C3×C4×C13
HallC32×C53⋊C13 ⋊ C4
HallC3×Dic3×C53 ⋊ C13
HallC32×C53 ⋊ C4×C13
SylowC53 ⋊ C3×Dic3×C13
SylowC32 ⋊ C4×C53⋊C13

Subgroups

subgroupG/H
center, hypercenterC2×C3D3×C53⋊C13
commutator, hypocenterC3×C53C3×C4×C13
FrattiniC2C3×D3×C53⋊C13
Fitting, socleC2×C32×C53C2×C13
prime radicalC2×C32×C53⋊C13C2
cosocleC2×C3×C53C2×C3×C13
LCSG ▷ C3×C53
UCSC1 ◁ C2×C3

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 636

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 68);