Finite Group Databasebeta

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C2×C5×C13×D21 #19129889

order5460
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C22×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C13×D21
unambiguous semidirect product(C2×C3)⋊(C5×C13×D7)
unambiguous semidirect product(C2×C7)⋊(C5×D3×C13)

Splittings

Fitting, socleC2×C3×C5×C7×C13 ⋊ C2
derived, HallC3×C7 ⋊ C22×C5×C13
HallC3×C5×C7×C13 ⋊ C22
HallC5×C7×C13 ⋊ C2×D3
HallC3×C7×C13 ⋊ C22×C5
HallC3×C5×C13 ⋊ C2×D7
HallC3×C5×C7 ⋊ C22×C13
HallC7×C13 ⋊ C2×C5×D3
HallC3×C13 ⋊ C2×C5×D7
HallC5×C7 ⋊ C2×D3×C13
HallC3×C5 ⋊ C2×C13×D7
SylowC7 ⋊ C2×C5×D3×C13
SylowC3 ⋊ C2×C5×C13×D7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13D21
commutator, hypocenterC3×C7C22×C5×C13
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C13C2
LCSG ▷ C3×C7
UCSC1 ◁ C2×C5×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1560 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C13×D63, C2×C5×C13×C3⋊AGL(1,𝔽7), C2×C5×C3⋊#10587720, …
maximal normal subgroup ofC2×C5×C13×C3⋊AGL(1,𝔽7), C2×C5×C3⋊#10587720, C2×C5×C3⋊#10587721, …
maximal quotient ofC2×C5×C13×D63, C5×D3×C13×D21, C2×C5×C13×C3⋊D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 231);