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C7×C3⋊D255 #24924229

order10710
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C3

Aliases

direct productC7×C3⋊D255
unambiguous semidirect productC3⋊(C7×D255)
unambiguous semidirect productC5⋊(C7×C3⋊D51)
unambiguous semidirect productC17⋊(C7×C3⋊D15)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C2
derived, HallC32×C5×C17 ⋊ C2×C7
HallC32×C7×C17 ⋊ D5
HallC5×C7×C17 ⋊ C3⋊D3
HallC32×C5×C7 ⋊ D17
HallC32×C17 ⋊ C7×D5
HallC7×C17 ⋊ C3⋊D15
HallC5×C17 ⋊ C7×C3⋊D3
HallC32×C7 ⋊ D85
HallC32×C5 ⋊ C7×D17
HallC5×C7 ⋊ C3⋊D51
SylowC17 ⋊ C7×C3⋊D15
SylowC32 ⋊ C7×D85
SylowC5 ⋊ C7×C3⋊D51

Subgroups

subgroupG/H
center, hypercenterC7C3⋊D255
commutator, cosocle, hypocenterC32×C5×C17C2×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C17C2
LCSG ▷ C32×C5×C17
UCSC1 ◁ C7

96 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×#15690390, C7×#15690391, C7⋊#15690390, …
maximal normal subgroup ofC7×#15690390, C7×#15690391, C7⋊#15690390, …
maximal quotient ofC7×C3⋊Dic255, C2×C7×C3⋊D255

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 44);