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C7⋊C9×D85 #24924207

order10710
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7⋊C9×D85
unambiguous semidirect productC5⋊(D17×C7⋊C9)
unambiguous semidirect productC17⋊(D5×C7⋊C9)
unambiguous semidirect product(C7×D85)⋊C9

Splittings

derived, HallC5×C7×C17 ⋊ C2×C9
HallC5×C17×C7⋊C9 ⋊ C2
HallC7×D85 ⋊ C9
HallC17×C7⋊C9 ⋊ D5
HallC5×C7⋊C9 ⋊ D17
HallC7×C17 ⋊ C9×D5
HallC5×C17 ⋊ C2×C7⋊C9
HallC5×C7 ⋊ C9×D17
SylowC17 ⋊ D5×C7⋊C9
SylowC7 ⋊ C9×D85
SylowC5 ⋊ D17×C7⋊C9

Subgroups

subgroupG/H
center, Frattini, hypercenterC3ΓL(1,𝔽8)×D85
commutator, hypocenterC5×C7×C17C2×C9
Fitting, socle, cosocleC3×C5×C7×C17C2×C3
prime radicalC3×C7×D85C3
LCSG ▷ C5×C7×C17
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C7⋊C9)⋊#66775, (C7⋊C9)⋊#66776, C7⋊C9×#66775, …
maximal normal subgroup of(C7⋊C9)⋊#66775, (C7⋊C9)⋊#66776, C7⋊C9×#66775, …
maximal quotient ofC7⋊C9×Dic85, C2×C7⋊C9×D85

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 22);