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C2×C3×C7×C43⋊C3 #19129395

order5418
isoclinismisoclinic class of C43⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C7×C43⋊C3

Splittings

Fitting, socleC2×C3×C7×C43 ⋊ C3
derived, SylowC43 ⋊ C2×C32×C7
HallC2×C7×C43 ⋊ C32
HallC7×C43 ⋊ C2×C32
HallC2×C43 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7C43⋊C3
commutator, hypocenterC43C2×C32×C7
FrattiniC1G
Fitting, socleC2×C3×C7×C43C3
LCSG ▷ C43
UCSC1 ◁ C2×C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

714 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C7×(C43⋊C3)⋊C4, C3×(C43⋊C3)⋊Dic7, C3×Dic7×C43⋊C3, …
maximal normal subgroup ofC3×C7×(C43⋊C3)⋊C4, C3×(C43⋊C3)⋊Dic7, C3×Dic7×C43⋊C3, …
maximal quotient ofC3×C4×C7×C43⋊C3, C22×C3×C7×C43⋊C3, C3×C7×D5×C43⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5418, 74);