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C2×C7×D67⋊C3 #19150602

order5628
isoclinismisoclinic class of D67⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D67⋊C3
unambiguous semidirect productD67⋊(C2×C3×C7)
unambiguous semidirect product(C67⋊C3)⋊(C22×C7)
unambiguous semidirect product(C2×D67)⋊(C3×C7)
unambiguous semidirect product(C2×C67⋊C3)⋊(C2×C7)

Splittings

Fitting, socleC2×C7×C67 ⋊ C2×C3
derived, SylowC67 ⋊ C22×C3×C7
HallC2×C7×D67 ⋊ C3
HallC7×C67⋊C3 ⋊ C22
HallC7×C67 ⋊ C22×C3
HallC2×D67 ⋊ C3×C7
HallC67⋊C3 ⋊ C22×C7

Subgroups

subgroupG/H
center, hypercenterC2×C7D67⋊C3
commutator, hypocenterC67C22×C3×C7
FrattiniC1G
Fitting, socleC2×C7×C67C2×C3
LCSG ▷ C67
UCSC1 ◁ C2×C7

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

238 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×ΓL(1,𝔽8)×D67⋊C3, D3×C7×D67⋊C3, C2×C3×C7×D67⋊C3, …
maximal normal subgroup ofC2×ΓL(1,𝔽8)×D67⋊C3, C2×C3×C7×D67⋊C3, C2×C5×C7×D67⋊C3
maximal quotient ofC2×C7×D67⋊C9, D3×C7×D67⋊C3, C2×C3×C7×D67⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5628, 30);