Finite Group Databasebeta

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C2×C5×C7×C3⋊D51 #36339587

order21420
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C5×C7×C3⋊D51
unambiguous semidirect product(C2×C3)⋊(C5×C7×D51)
unambiguous semidirect product(C2×C17)⋊(C5×C7×C3⋊D3)

Splittings

Fitting, socleC2×C32×C5×C7×C17 ⋊ C2
derived, HallC32×C17 ⋊ C22×C5×C7
HallC32×C5×C7×C17 ⋊ C22
HallC32×C7×C17 ⋊ C22×C5
HallC32×C5×C17 ⋊ C22×C7
HallC5×C7×C17 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C2×D17
HallC7×C17 ⋊ C2×C5×C3⋊D3
HallC5×C17 ⋊ C2×C7×C3⋊D3
HallC32×C7 ⋊ C2×C5×D17
HallC32×C5 ⋊ C2×C7×D17
SylowC17 ⋊ C2×C5×C7×C3⋊D3
SylowC32 ⋊ C2×C5×C7×D17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7C3⋊D51
commutator, cosocle, hypocenterC32×C17C22×C5×C7
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C17C2
LCSG ▷ C32×C17
UCSC1 ◁ C2×C5×C7

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10710

Conjugacy classes & character table

5460 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 419);