C₃×C₁₁×D₁₈₇ #27134668

order	12342
isoclinism	isoclinic class of D₁₈₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₁₁×D₁₈₇
unambiguous semidirect product	C₁₁⋊(C₃×C₁₁×D₁₇)
unambiguous semidirect product	C₁₇⋊(C₃×C₁₁×D₁₁)

Splittings

Fitting, socle, Hall	C₃×C₁₁²×C₁₇ ⋊ C₂
derived	C₁₁×C₁₇ ⋊ C₂×C₃×C₁₁
Hall	C₁₁²×C₁₇ ⋊ C₂×C₃
Hall	C₃×C₁₁² ⋊ D₁₇
Sylow	C₁₁² ⋊ C₃×D₁₇
Hall	C₃×C₁₇ ⋊ C₁₁×D₁₁
Sylow	C₁₇ ⋊ C₃×C₁₁×D₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₁	D₁₈₇
commutator, cosocle, hypocenter	C₁₁×C₁₇	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₁²×C₁₇	C₂
LCS	G ▷ C₁₁×C₁₇
UCS	C₁ ◁ C₃×C₁₁

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:

(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)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41,42);(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)(29,30,32,34,36,38,39,37,35,33,31)

Conjugacy classes & character table

3135 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₁×D₁₁×D₁₇, C₃×D₁₁×D₁₈₇, C₃×(C₁₁⋊D₁₁)⋊D₁₇, …
maximal normal subgroup of	C₃×C₁₁×D₁₁×D₁₇, C₃×D₁₁×D₁₈₇, C₃×(C₁₁⋊D₁₁)⋊D₁₇, …
maximal quotient of	C₃×C₁₁×Dic₁₈₇, C₂×C₃×C₁₁×D₁₈₇, C₉×C₁₁×D₁₈₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12342, 24);

C3×C11×D187 #27134668