Finite Group Databasebeta

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C3×C7×D255 #24924237

order10710
isoclinismisoclinic class of D255
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D255
unambiguous semidirect productC3⋊(C3×C7×D85)
unambiguous semidirect productC5⋊(C3×C7×D51)
unambiguous semidirect productC17⋊(C3×C7×D15)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C2
derivedC3×C5×C17 ⋊ C2×C3×C7
HallC32×C7×C17 ⋊ D5
HallC32×C5×C17 ⋊ C2×C7
HallC5×C7×C17 ⋊ C3×D3
HallC32×C5×C7 ⋊ D17
HallC32×C17 ⋊ C7×D5
HallC7×C17 ⋊ C3×D15
HallC5×C17 ⋊ C3×D3×C7
HallC32×C7 ⋊ D85
HallC32×C5 ⋊ C7×D17
HallC5×C7 ⋊ C3×D51
SylowC17 ⋊ C3×C7×D15
SylowC32 ⋊ C7×D85
SylowC5 ⋊ C3×C7×D51

Subgroups

subgroupG/H
center, hypercenterC3×C7D255
commutator, cosocle, hypocenterC3×C5×C17C2×C3×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C17C2
LCSG ▷ C3×C5×C17
UCSC1 ◁ C3×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2709 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C7×D15×D17, C3×D7×D255, C3×D119⋊D15, …
maximal normal subgroup ofC3×C7×D15×D17, C3×D7×D255, C3×D119⋊D15, …
maximal quotient ofC3×C7×Dic255, C2×C3×C7×D255

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 52);