Finite Group Databasebeta

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C7×C17×D45 #24924199

order10710
isoclinismisoclinic class of D45
automorphism?
homologyAbelianization (H1) = C2×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC7×C17×D45
unambiguous semidirect productC5⋊(C7×C17×D9)
unambiguous semidirect productC9⋊(C7×D5×C17)

Splittings

Fitting, HallC5×C7×C9×C17 ⋊ C2
derived, HallC5×C9 ⋊ C2×C7×C17
HallC7×C9×C17 ⋊ D5
HallC5×C9×C17 ⋊ C2×C7
HallC5×C7×C17 ⋊ D9
HallC5×C7×C9 ⋊ C2×C17
HallC9×C17 ⋊ C7×D5
HallC5×C17 ⋊ C7×D9
HallC7×C9 ⋊ D5×C17
HallC5×C7 ⋊ C17×D9
SylowC9 ⋊ C7×D5×C17
SylowC5 ⋊ C7×C17×D9

Subgroups

subgroupG/H
center, hypercenterC7×C17D45
commutator, cosocle, hypocenterC5×C9C2×C7×C17
FrattiniC3C7×C17×D15
FittingC5×C7×C9×C17C2
socleC3×C5×C7×C17D3
LCSG ▷ C5×C9
UCSC1 ◁ C7×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2856 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D17×D45, D7×C17×D45, D45×D119, …
maximal normal subgroup ofC7×D17×D45, D7×C17×D45, D45×D119, …
maximal quotient ofC7×C17×Dic45, C2×C7×C17×D45

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 14);