C₉×D₂₁₇ #16840870

order	3906
isoclinism	isoclinic class of D₂₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₉×D₂₁₇

Splittings

Fitting, Hall	C₇×C₉×C₃₁ ⋊ C₂
derived, Hall	C₇×C₃₁ ⋊ C₂×C₉
Hall	C₉×C₃₁ ⋊ D₇
Hall	C₇×C₉ ⋊ D₃₁
Sylow	C₃₁ ⋊ C₉×D₇
Sylow	C₇ ⋊ C₉×D₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₂₁₇
commutator, hypocenter	C₇×C₃₁	C₂×C₉
Frattini	C₃	C₃×D₂₁₇
Fitting	C₇×C₉×C₃₁	C₂
socle, cosocle	C₃×C₇×C₃₁	C₂×C₃
prime radical	C₃×D₂₁₇	C₃
LCS	G ▷ C₇×C₃₁
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1953

A minimal faithful permutation representation — 2 generators on 47 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);(11,16)(12,15)(13,14)(18,47)(19,46)(20,45)(21,44)(22,43)(23,42)(24,41)(25,40)(26,39)(27,38)(28,37)(29,36)(30,35)(31,34)(32,33)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×C₉×D₂₁₇, C₉×D₁₀₈₅, C₉×C₇⋊(D₃₁⋊C₅), …
maximal normal subgroup of	C₅×C₉×D₂₁₇, C₉×C₇⋊(D₃₁⋊C₅), C₇×C₉×D₂₁₇
maximal quotient of	C₅×C₉×D₂₁₇, C₉×D₁₀₈₅, C₉×D₁₅₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3906, 20);

C9×D217 #16840870