C₃×C₁₁×C₁₇×D₁₁ #27134669

order	12342
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₁×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₁₁×C₁₇×D₁₁
unambiguous semidirect product	C₁₁⋊(C₂×C₃×C₁₁×C₁₇)

Splittings

Fitting, socle, Hall	C₃×C₁₁²×C₁₇ ⋊ C₂
derived	C₁₁ ⋊ C₂×C₃×C₁₁×C₁₇
Hall	C₁₁²×C₁₇ ⋊ C₂×C₃
Hall	C₃×C₁₁² ⋊ C₂×C₁₇
Sylow	C₁₁² ⋊ C₂×C₃×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₁×C₁₇	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₃×C₁₁×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₁²×C₁₇	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₃×C₁₁×C₁₇

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 1122

A minimal faithful permutation representation — 2 generators on 42 points:

(1,2,3,4,5,6,7,8,9,10,11)(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);(12,13,15,17,19,21,22,20,18,16,14)

Conjugacy classes & character table

3927 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₁×D₁₁×D₁₇, C₃×C₁₇×D₁₁², C₃×D₁₁×D₁₈₇, …
maximal normal subgroup of	C₃×C₁₁×D₁₁×D₁₇, C₃×C₁₇×D₁₁², C₃×D₁₁×D₁₈₇, …
maximal quotient of	C₃×C₁₁×C₁₇×Dic₁₁, C₂×C₃×C₁₁×C₁₇×D₁₁, C₉×C₁₁×C₁₇×D₁₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12342, 25);

C3×C11×C17×D11 #27134669