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C5×C7×C3⋊D51 #24924233

order10710
isoclinismisoclinic class of C3⋊D51
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC5×C7×C3⋊D51
unambiguous semidirect productC3⋊(C5×C7×D51)
unambiguous semidirect productC17⋊(C5×C7×C3⋊D3)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C2
derived, HallC32×C17 ⋊ C2×C5×C7
HallC32×C7×C17 ⋊ C2×C5
HallC32×C5×C17 ⋊ C2×C7
HallC5×C7×C17 ⋊ C3⋊D3
HallC32×C5×C7 ⋊ D17
HallC7×C17 ⋊ C5×C3⋊D3
HallC5×C17 ⋊ C7×C3⋊D3
HallC32×C7 ⋊ C5×D17
HallC32×C5 ⋊ C7×D17
SylowC17 ⋊ C5×C7×C3⋊D3
SylowC32 ⋊ C5×C7×D17

Subgroups

subgroupG/H
center, hypercenterC5×C7C3⋊D51
commutator, cosocle, hypocenterC32×C17C2×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C17C2
LCSG ▷ C32×C17
UCSC1 ◁ C5×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2730 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×#10597479, C5×C7⋊#10597479, C7×#15690394, …
maximal normal subgroup ofC5×C7×#10597479, C5×C7⋊#10597479, C7×#15690394, …
maximal quotient ofC5×C7×C3⋊Dic51, C2×C5×C7×C3⋊D51

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 48);