Finite Group Databasebeta

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C32×D595 #24924243

order10710
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC32×D595
unambiguous semidirect productC5⋊(C32×D119)
unambiguous semidirect productC17⋊(C32×D35)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C2
derived, HallC5×C7×C17 ⋊ C2×C32
HallC32×C7×C17 ⋊ D5
HallC32×C5×C17 ⋊ D7
HallC32×C5×C7 ⋊ D17
HallC32×C17 ⋊ D35
HallC7×C17 ⋊ C32×D5
HallC5×C17 ⋊ C32×D7
HallC32×C7 ⋊ D85
HallC32×C5 ⋊ D119
HallC5×C7 ⋊ C32×D17
SylowC17 ⋊ C32×D35
SylowC7 ⋊ C32×D85
SylowC5 ⋊ C32×D119

Subgroups

subgroupG/H
center, hypercenterC32D595
commutator, cosocle, hypocenterC5×C7×C17C2×C32
FrattiniC1G
Fitting, socleC32×C5×C7×C17C2
LCSG ▷ C5×C7×C17
UCSC1 ◁ C32

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2691 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×D17×D35, C32×D7×D85, C32×D5×D119, …
maximal normal subgroup ofC32×D17×D35, C32×D7×D85, C32×D5×D119, …
maximal quotient ofC32×Dic595, C2×C32×D595

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 58);