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C2×D21×C59 #19097192

order4956
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C22×C59 · Schur multiplier (H2) = C2

Aliases

direct productC2×D21×C59
unambiguous semidirect product(C2×C3)⋊(D7×C59)
unambiguous semidirect product(C2×C7)⋊(D3×C59)

Splittings

Fitting, socleC2×C3×C7×C59 ⋊ C2
derived, HallC3×C7 ⋊ C22×C59
HallC3×C7×C59 ⋊ C22
HallC7×C59 ⋊ C2×D3
HallC3×C59 ⋊ C2×D7
SylowC7 ⋊ C2×D3×C59
SylowC3 ⋊ C2×D7×C59

Subgroups

subgroupG/H
center, hypercenterC2×C59D21
commutator, hypocenterC3×C7C22×C59
FrattiniC1G
Fitting, socleC2×C3×C7×C59C2
LCSG ▷ C3×C7
UCSC1 ◁ C2×C59

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1416 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C59×D63, C2×C59×C3⋊AGL(1,𝔽7), D3×D21×C59, …
maximal normal subgroup ofC2×C59×C3⋊AGL(1,𝔽7), C2×C3×D21×C59, C2×C5×D21×C59, …
maximal quotient ofC2×C59×D63, D3×D21×C59, C2×C59×C3⋊D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4956, 33);