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C7×D765 #24924200

order10710
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D765
unambiguous semidirect productC5⋊(C7×D153)
unambiguous semidirect productC9⋊(C7×D85)
unambiguous semidirect productC17⋊(C7×D45)

Splittings

Fitting, HallC5×C7×C9×C17 ⋊ C2
derived, HallC5×C9×C17 ⋊ C2×C7
HallC7×C9×C17 ⋊ D5
HallC5×C7×C17 ⋊ D9
HallC5×C7×C9 ⋊ D17
HallC9×C17 ⋊ C7×D5
HallC7×C17 ⋊ D45
HallC5×C17 ⋊ C7×D9
HallC7×C9 ⋊ D85
HallC5×C9 ⋊ C7×D17
HallC5×C7 ⋊ D153
SylowC17 ⋊ C7×D45
SylowC9 ⋊ C7×D85
SylowC5 ⋊ C7×D153

Subgroups

subgroupG/H
center, hypercenterC7D765
commutator, cosocle, hypocenterC5×C9×C17C2×C7
FrattiniC3C7×D255
FittingC5×C7×C9×C17C2
socleC3×C5×C7×C17D3
LCSG ▷ C5×C9×C17
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2688 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D17×D45, D7×D765, D119⋊D45, …
maximal normal subgroup ofC7×D17×D45, D7×D765, D119⋊D45, …
maximal quotient ofC7×Dic765, C2×C7×D765

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 15);