Finite Group Databasebeta

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C32×C17×D35 #24924244

order10710
isoclinismisoclinic class of D35
automorphism?
homologyAbelianization (H1) = C2×C32×C17 · Schur multiplier (H2) = C3

Aliases

direct productC32×C17×D35
unambiguous semidirect productC5⋊(C32×D7×C17)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C2
derived, HallC5×C7 ⋊ C2×C32×C17
HallC32×C7×C17 ⋊ D5
HallC32×C5×C17 ⋊ D7
HallC5×C7×C17 ⋊ C2×C32
HallC32×C5×C7 ⋊ C2×C17
HallC7×C17 ⋊ C32×D5
HallC5×C17 ⋊ C32×D7
HallC32×C7 ⋊ D5×C17
HallC32×C5 ⋊ D7×C17
SylowC7 ⋊ C32×D5×C17
SylowC5 ⋊ C32×D7×C17

Subgroups

subgroupG/H
center, hypercenterC32×C17D35
commutator, cosocle, hypocenterC5×C7C2×C32×C17
FrattiniC1G
Fitting, socleC32×C5×C7×C17C2
LCSG ▷ C5×C7
UCSC1 ◁ C32×C17

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2907 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×D17×D35, C32×D5×D7×C17, C32×D35⋊D17, …
maximal normal subgroup ofC32×D17×D35, C32×D5×D7×C17, C32×D35⋊D17, …
maximal quotient ofC32×C17×Dic35, C2×C32×C17×D35

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 59);