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C5×D1071 #24924198

order10710
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D1071
unambiguous semidirect productC7⋊(C5×D153)
unambiguous semidirect productC9⋊(C5×D119)
unambiguous semidirect productC17⋊(C5×D63)

Splittings

Fitting, HallC5×C7×C9×C17 ⋊ C2
derived, HallC7×C9×C17 ⋊ C2×C5
HallC5×C9×C17 ⋊ D7
HallC5×C7×C17 ⋊ D9
HallC5×C7×C9 ⋊ D17
HallC9×C17 ⋊ C5×D7
HallC7×C17 ⋊ C5×D9
HallC5×C17 ⋊ D63
HallC7×C9 ⋊ C5×D17
HallC5×C9 ⋊ D119
HallC5×C7 ⋊ D153
SylowC17 ⋊ C5×D63
SylowC9 ⋊ C5×D119
SylowC7 ⋊ C5×D153

Subgroups

subgroupG/H
center, hypercenterC5D1071
commutator, cosocle, hypocenterC7×C9×C17C2×C5
FrattiniC3C5×D357
FittingC5×C7×C9×C17C2
socleC3×C5×C7×C17D3
LCSG ▷ C7×C9×C17
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2685 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D17×D63, C5×D7×D153, C5×D9×D119, …
maximal normal subgroup ofC5×D17×D63, C5×D7×D153, C5×D9×D119, …
maximal quotient ofC5×Dic1071, C2×C5×D1071

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 13);