C₅×C₉×D₄₃ #16838826

order	3870
isoclinism	isoclinic class of D₄₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×C₉×D₄₃

Splittings

Fitting, Hall	C₅×C₉×C₄₃ ⋊ C₂
derived, Sylow	C₄₃ ⋊ C₂×C₅×C₉
Hall	C₉×C₄₃ ⋊ C₂×C₅
Hall	C₅×C₄₃ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉	D₄₃
commutator, hypocenter	C₄₃	C₂×C₅×C₉
Frattini	C₃	C₃×C₅×D₄₃
Fitting	C₅×C₉×C₄₃	C₂
socle	C₃×C₅×C₄₃	C₂×C₃
prime radical	C₃×C₅×D₄₃	C₃
cosocle	C₃×C₄₃	C₂×C₃×C₅
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₅×C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 1935

A minimal faithful permutation representation — 2 generators on 57 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57);(16,57)(17,56)(18,55)(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)

Conjugacy classes & character table

1035 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₂₅×D₄₃, C₅²×C₉×D₄₃, C₅×C₉×D₂₁₅, …
maximal normal subgroup of	C₉×C₂₅×D₄₃, C₅²×C₉×D₄₃, C₅×C₇×C₉×D₄₃, …
maximal quotient of	C₉×C₂₅×D₄₃, C₅²×C₉×D₄₃, C₅×C₉×D₂₁₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3870, 6);

C5×C9×D43 #16838826