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C7×D43⋊C3 #14268583

order1806
isoclinismisoclinic class of D43⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D43⋊C3

Splittings

Fitting, socle, HallC7×C43 ⋊ C2×C3
derived, SylowC43 ⋊ C2×C3×C7
HallC7×C43⋊C3 ⋊ C2
HallC7×D43 ⋊ C3
HallC43⋊C3 ⋊ C2×C7
HallD43 ⋊ C3×C7

Subgroups

subgroupG/H
center, hypercenterC7D43⋊C3
commutator, cosocle, hypocenterC43C2×C3×C7
FrattiniC1G
Fitting, socleC7×C43C2×C3
LCSG ▷ C43
UCSC1 ◁ C7

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 301

A minimal faithful permutation representation — 2 generators on 50 points:

(1,2,3,4,5,6,7)(9,13,14,10,11,15)(12,21,22,16,17,31)(18,34,35,24,25,43)(19,33,29,27,23,20)(26,39,41,30,32,44)(28,45,46,37,36,40)(38,48,49,47,42,50);(8,9,12,18,26,29,14,13,19,28,38,46,22,33,21,32,42,49,35,44,45,34,25,36,41,43,50,48,39,17,23,31,40,47,37,27,11,15,20,30,24,16,10)

Conjugacy classes & character table

91 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD7×D43⋊C3, C2×C7×D43⋊C3, (D43⋊C3)⋊C49, …
maximal normal subgroup ofD7×D43⋊C3, C2×C7×D43⋊C3, (D43⋊C3)⋊C49, …
maximal quotient ofC7×(C43⋊C3)⋊C4, C2×C7×D43⋊C3, C49×D43⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1806, 7);