Finite Group Databasebeta

← Prev (#37613654) Next (#37613656) →

C3×Dic3×C13×C53 #37613655

order24804
automorphism?
homologyAbelianization (H1) = C3×C4×C13×C53 · Schur multiplier (H2) = C1

Aliases

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

Splittings

derivedC3 ⋊ C3×C4×C13×C53
HallC32×C13×C53 ⋊ C4
HallC32×C53 ⋊ C4×C13
HallC32×C13 ⋊ C4×C53
SylowC32 ⋊ C4×C13×C53

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13×C53D3
commutator, hypocenterC3C3×C4×C13×C53
FrattiniC2C3×D3×C13×C53
Fitting, socle, prime radicalC2×C32×C13×C53C2
cosocleC2×C3C2×C3×C13×C53
LCSG ▷ C3
UCSC1 ◁ C2×C3×C13×C53

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8268

Conjugacy classes & character table

12402 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 87);