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C4×C43⋊C7 #11925836

order1204
isoclinismisoclinic class of C43⋊C7
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC4×C43⋊C7
unambiguous semidirect product(C4×C43)⋊C7

Splittings

Fitting, HallC4×C43 ⋊ C7
derived, SylowC43 ⋊ C4×C7

Subgroups

subgroupG/H
center, hypercenterC4C43⋊C7
commutator, hypocenterC43C4×C7
FrattiniC2C2×C43⋊C7
FittingC4×C43C7
socle, cosocleC2×C43C2×C7
prime radicalC2×C43⋊C7C2
LCSG ▷ C43
UCSC1 ◁ C4

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 172

A minimal faithful permutation representation — 2 generators on 47 points:

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×(C43⋊C3)⋊C7, Dic3×C43⋊C7, C3×C4×C43⋊C7, …
maximal normal subgroup ofC4×(C43⋊C3)⋊C7, C3×C4×C43⋊C7, C4×C13×C43⋊C7, …
maximal quotient ofDic3×C43⋊C7, C3×C4×C43⋊C7, #157×C43⋊C7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1204, 2);