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C₉×D₇×C₁₇ #14523871

order	2142
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₇×C₁₇

Splittings

Fitting, Hall	C₇×C₉×C₁₇ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₉×C₁₇
Hall	C₇×C₁₇ ⋊ C₂×C₉
Hall	C₇×C₉ ⋊ C₂×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₇	D₇
commutator, hypocenter	C₇	C₂×C₉×C₁₇
Frattini	C₃	C₃×D₇×C₁₇
Fitting	C₇×C₉×C₁₇	C₂
socle	C₃×C₇×C₁₇	C₂×C₃
prime radical	C₃×D₇×C₁₇	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₉×C₁₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 1071

A minimal faithful permutation representation — 2 generators on 33 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);(11,16)(12,15)(13,14)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₉×D₇×D₁₇, D₇×C₁₇×D₉, D₇×D₁₅₃, …
maximal normal subgroup of	C₉×D₇×D₁₇, D₇×C₁₇×D₉, D₇×D₁₅₃, …
maximal quotient of	C₉×C₁₇×Dic₇, C₂×C₉×D₇×C₁₇, C₉×C₁₇×D₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2142, 7);