Finite Group Databasebeta

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C32×C7×D85 #24924245

order10710
isoclinismisoclinic class of D85
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7×D85
unambiguous semidirect productC5⋊(C32×C7×D17)
unambiguous semidirect productC17⋊(C32×C7×D5)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C2
derived, HallC5×C17 ⋊ C2×C32×C7
HallC32×C7×C17 ⋊ D5
HallC32×C5×C17 ⋊ C2×C7
HallC5×C7×C17 ⋊ C2×C32
HallC32×C5×C7 ⋊ D17
HallC32×C17 ⋊ C7×D5
HallC7×C17 ⋊ C32×D5
HallC32×C5 ⋊ C7×D17
HallC5×C7 ⋊ C32×D17
SylowC17 ⋊ C32×C7×D5
SylowC5 ⋊ C32×C7×D17

Subgroups

subgroupG/H
center, hypercenterC32×C7D85
commutator, cosocle, hypocenterC5×C17C2×C32×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C17C2
LCSG ▷ C5×C17
UCSC1 ◁ C32×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2772 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C7×#66775, C32×C7×#66776, C32×C7⋊#66775, …
maximal normal subgroup ofC32×C7×#66775, C32×C7×#66776, C32×C7⋊#66775, …
maximal quotient ofC32×C7×Dic85, C2×C32×C7×D85

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 60);