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C2×C5×C17×C7⋊C9 #24924187

order10710
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C17×C7⋊C9
unambiguous semidirect product(C2×C7)⋊(C5×C9×C17)
unambiguous semidirect product(C2×C5×C7)⋊(C9×C17)
unambiguous semidirect product(C2×C7×C17)⋊(C5×C9)
unambiguous semidirect product(C2×C5×C7×C17)⋊C9

Splittings

derived, SylowC7 ⋊ C2×C5×C9×C17
HallC2×C5×C7×C17 ⋊ C9
HallC5×C7×C17 ⋊ C2×C9
HallC2×C7×C17 ⋊ C5×C9
HallC7×C17 ⋊ C2×C5×C9
HallC2×C5×C7 ⋊ C9×C17
HallC5×C7 ⋊ C2×C9×C17
HallC2×C7 ⋊ C5×C9×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C17ΓL(1,𝔽8)
commutator, hypocenterC7C2×C5×C9×C17
FrattiniC3C2×C5×C17×ΓL(1,𝔽8)
Fitting, socle, prime radicalC2×C3×C5×C7×C17C3
cosocleC3×C7C2×C3×C5×C17
LCSG ▷ C7
UCSC1 ◁ C2×C3×C5×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2550 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C17×C7⋊C9, C5×C7⋊C9×Dic17, C5×C17×Dic7⋊C9, …
maximal normal subgroup ofC4×C5×C17×C7⋊C9, C5×C7⋊C9×Dic17, C5×C17×Dic7⋊C9, …
maximal quotient ofC4×C5×C17×C7⋊C9, C22×C5×C17×C7⋊C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 2);