Finite Group Databasebeta

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C3×C5×C7×D51 #24924241

order10710
isoclinismisoclinic class of D51
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C7×D51
unambiguous semidirect productC3⋊(C3×C5×C7×D17)
unambiguous semidirect productC17⋊(C3×C5×D3×C7)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C2
derivedC3×C17 ⋊ C2×C3×C5×C7
HallC32×C7×C17 ⋊ C2×C5
HallC32×C5×C17 ⋊ C2×C7
HallC5×C7×C17 ⋊ C3×D3
HallC32×C5×C7 ⋊ D17
HallC32×C17 ⋊ C2×C5×C7
HallC7×C17 ⋊ C3×C5×D3
HallC5×C17 ⋊ C3×D3×C7
HallC32×C7 ⋊ C5×D17
HallC32×C5 ⋊ C7×D17
SylowC17 ⋊ C3×C5×D3×C7
SylowC32 ⋊ C5×C7×D17

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7D51
commutator, cosocle, hypocenterC3×C17C2×C3×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C17C2
LCSG ▷ C3×C17
UCSC1 ◁ C3×C5×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2835 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D3×C7×D17, C3×C5×D7×D51, C3×C5×D21⋊D17, …
maximal normal subgroup ofC3×C5×D3×C7×D17, C3×C5×D7×D51, C3×C5×D21⋊D17, …
maximal quotient ofC3×C5×C7×Dic51, C2×C3×C5×C7×D51

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 56);