Finite Group Databasebeta

← Prev (#37590390) Next (#37590392) →

C3×C5×Dic3×C137 #37590391

order24660
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C137 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic3×C137
unambiguous semidirect productC3⋊(C3×C4×C5×C137)

Splittings

derivedC3 ⋊ C3×C4×C5×C137
HallC32×C5×C137 ⋊ C4
HallC32×C137 ⋊ C4×C5
HallC32×C5 ⋊ C4×C137
SylowC32 ⋊ C4×C5×C137

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C137D3
commutator, hypocenterC3C3×C4×C5×C137
FrattiniC2C3×C5×D3×C137
Fitting, socle, prime radicalC2×C32×C5×C137C2
cosocleC2×C3C2×C3×C5×C137
LCSG ▷ C3
UCSC1 ◁ C2×C3×C5×C137

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8220

Conjugacy classes & character table

12330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24660, 45);