Finite Group Databasebeta

← Prev (#30629028) Next (#30629030) →

C3×C31×D85 #30629029

order15810
isoclinismisoclinic class of D85
automorphism?
homologyAbelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C1

Aliases

direct productC3×C31×D85
unambiguous semidirect productC5⋊(C3×C31×D17)
unambiguous semidirect productC17⋊(C3×D5×C31)

Splittings

Fitting, socle, HallC3×C5×C17×C31 ⋊ C2
derived, HallC5×C17 ⋊ C2×C3×C31
HallC5×C17×C31 ⋊ C2×C3
HallC3×C17×C31 ⋊ D5
HallC17×C31 ⋊ C3×D5
HallC3×C5×C31 ⋊ D17
HallC3×C5×C17 ⋊ C2×C31
HallC5×C31 ⋊ C3×D17
HallC3×C17 ⋊ D5×C31
SylowC17 ⋊ C3×D5×C31
HallC3×C5 ⋊ C31×D17
SylowC5 ⋊ C3×C31×D17

Subgroups

subgroupG/H
center, hypercenterC3×C31D85
commutator, cosocle, hypocenterC5×C17C2×C3×C31
FrattiniC1G
Fitting, socleC3×C5×C17×C31C2
LCSG ▷ C5×C17
UCSC1 ◁ C3×C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

4092 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C31×#66775, C3×C31⋊#66775, C3×C31×#66776, …
maximal normal subgroup ofC3×C31×#66775, C3×C31⋊#66775, C3×C31×#66776, …
maximal quotient ofC3×C31×Dic85, C2×C3×C31×D85

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15810, 10);