Finite Group Databasebeta

← Prev (#22551292) Next (#22551294) →

C32×C13×D35 #22551293

order8190
isoclinismisoclinic class of D35
automorphism?
homologyAbelianization (H1) = C2×C32×C13 · Schur multiplier (H2) = C3

Aliases

direct productC32×C13×D35
unambiguous semidirect productC5⋊(C32×C13×D7)

Splittings

Fitting, socle, HallC32×C5×C7×C13 ⋊ C2
derived, HallC5×C7 ⋊ C2×C32×C13
HallC32×C7×C13 ⋊ D5
HallC32×C5×C13 ⋊ D7
HallC5×C7×C13 ⋊ C2×C32
HallC32×C5×C7 ⋊ C2×C13
HallC7×C13 ⋊ C32×D5
HallC5×C13 ⋊ C32×D7
HallC32×C7 ⋊ D5×C13
HallC32×C5 ⋊ C13×D7
SylowC7 ⋊ C32×D5×C13
SylowC5 ⋊ C32×C13×D7

Subgroups

subgroupG/H
center, hypercenterC32×C13D35
commutator, hypocenterC5×C7C2×C32×C13
FrattiniC1G
Fitting, socleC32×C5×C7×C13C2
LCSG ▷ C5×C7
UCSC1 ◁ C32×C13

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2223 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×D13×D35, C32×D5×C13×D7, C32×D35⋊D13, …
maximal normal subgroup ofC32×D13×D35, C32×D5×C13×D7, C32×D35⋊D13, …
maximal quotient ofC32×C13×Dic35, C2×C32×C13×D35

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8190, 127);