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C2×C5×C3⋊D21 #11929576

order1260
isoclinismisoclinic class of C3⋊D21
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3

Aliases

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

Splittings

Fitting, socleC2×C32×C5×C7 ⋊ C2
derived, HallC32×C7 ⋊ C22×C5
HallC32×C5×C7 ⋊ C22
HallC32×C5 ⋊ C2×D7
HallC5×C7 ⋊ C2×C3⋊D3
SylowC32 ⋊ C2×C5×D7
SylowC7 ⋊ C2×C5×C3⋊D3

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊D21
commutator, cosocle, hypocenterC32×C7C22×C5
FrattiniC1G
Fitting, socleC2×C32×C5×C7C2
LCSG ▷ C32×C7
UCSC1 ◁ C2×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 630

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,𝔽11)×C3⋊D21, C2×C3⋊(C3⋊(C7⋊AGL(1,𝔽11))), C2×C11⋊C5×C3⋊D21, …
maximal normal subgroup ofC2×C5×C11×C3⋊D21, C2×C5×C13×C3⋊D21, C2×C5×C17×C3⋊D21, …
maximal quotient ofAGL(1,𝔽11)×C3⋊D21, C2×C3⋊(C3⋊(C7⋊AGL(1,𝔽11))), C2×C11⋊C5×C3⋊D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1260, 128);