Finite Group Databasebeta

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C32×C5×D119 #24924247

order10710
isoclinismisoclinic class of D119
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×D119
unambiguous semidirect productC17⋊(C32×C5×D7)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C2
derived, HallC7×C17 ⋊ C2×C32×C5
HallC32×C7×C17 ⋊ C2×C5
HallC32×C5×C17 ⋊ D7
HallC5×C7×C17 ⋊ C2×C32
HallC32×C5×C7 ⋊ D17
HallC32×C17 ⋊ C5×D7
HallC5×C17 ⋊ C32×D7
HallC32×C7 ⋊ C5×D17
HallC5×C7 ⋊ C32×D17
SylowC17 ⋊ C32×C5×D7
SylowC7 ⋊ C32×C5×D17

Subgroups

subgroupG/H
center, hypercenterC32×C5D119
commutator, cosocle, hypocenterC7×C17C2×C32×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C17C2
LCSG ▷ C7×C17
UCSC1 ◁ C32×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2745 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C5×D7×D17, C32×D5×D119, C32×D35⋊D17, …
maximal normal subgroup ofC32×C5×D7×D17, C32×D5×D119, C32×D35⋊D17, …
maximal quotient ofC32×C5×Dic119, C2×C32×C5×D119

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 62);