C₉×D₂₀₃ #16814495

order	3654
isoclinism	isoclinic class of D₂₀₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₂₀₃
unambiguous semidirect product	C₂₉⋊(C₉×D₇)

Splittings

Fitting, Hall	C₇×C₉×C₂₉ ⋊ C₂
derived, Hall	C₇×C₂₉ ⋊ C₂×C₉
Hall	C₉×C₂₉ ⋊ D₇
Hall	C₇×C₉ ⋊ D₂₉
Sylow	C₂₉ ⋊ C₉×D₇
Sylow	C₇ ⋊ C₉×D₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₂₀₃
commutator, hypocenter	C₇×C₂₉	C₂×C₉
Frattini	C₃	C₃×D₂₀₃
Fitting	C₇×C₉×C₂₉	C₂
socle, cosocle	C₃×C₇×C₂₉	C₂×C₃
prime radical	C₃×D₂₀₃	C₃
LCS	G ▷ C₇×C₂₉
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1827

A minimal faithful permutation representation — 2 generators on 45 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);(11,16)(12,15)(13,14)(18,45)(19,44)(20,43)(21,42)(22,41)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×C₉×D₂₀₃, C₉×D₁₀₁₅, C₉×D₁₄₂₁, …
maximal normal subgroup of	C₅×C₉×D₂₀₃, C₉×C₇⋊(D₂₉⋊C₇), C₇×C₉×D₂₀₃
maximal quotient of	C₅×C₉×D₂₀₃, C₉×D₁₀₁₅, C₉×D₁₄₂₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3654, 12);

C9×D203 #16814495