Finite Group Databasebeta

← Prev (#37613644) Next (#37613646) →

Dic3×C13⋊C3×C53 #37613645

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

Aliases

direct productDic3×C13⋊C3×C53
unambiguous semidirect productC3⋊(C4×C13⋊C3×C53)
unambiguous semidirect product(Dic3×C13)⋊(C3×C53)
unambiguous semidirect product(Dic3×C13×C53)⋊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×C53D3×C13⋊C3
commutator, hypocenterC3×C13C3×C4×C53
FrattiniC2D3×C13⋊C3×C53
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

2226 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 77);