Finite Group Databasebeta

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C7×C9×D5×C17 #24924191

order10710
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C7×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×D5×C17
unambiguous semidirect productC5⋊(C2×C7×C9×C17)

Splittings

Fitting, HallC5×C7×C9×C17 ⋊ C2
derived, SylowC5 ⋊ C2×C7×C9×C17
HallC5×C9×C17 ⋊ C2×C7
HallC5×C7×C17 ⋊ C2×C9
HallC5×C7×C9 ⋊ C2×C17
HallC5×C17 ⋊ C2×C7×C9
HallC5×C9 ⋊ C2×C7×C17
HallC5×C7 ⋊ C2×C9×C17

Subgroups

subgroupG/H
center, hypercenterC7×C9×C17D5
commutator, hypocenterC5C2×C7×C9×C17
FrattiniC3C3×C7×D5×C17
FittingC5×C7×C9×C17C2
socleC3×C5×C7×C17C2×C3
prime radicalC3×C7×D5×C17C3
cosocleC3×C5C2×C3×C7×C17
LCSG ▷ C5
UCSC1 ◁ C7×C9×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4284 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×C9×C17×AGL(1,𝔽5), C7×C9×#66774, C9×C17×C7⋊AGL(1,𝔽5), …
maximal normal subgroup ofC7×C9×C17×AGL(1,𝔽5), C7×C9×#66774, C9×C17×C7⋊AGL(1,𝔽5), …
maximal quotient ofC7×C9×C17×Dic5, C2×C7×C9×D5×C17

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 6);