C₂×C₁₁×#4294 #16836765

order	3762
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₂×C₁₁×#4294

Splittings

derived, Sylow	C₁₉ ⋊ C₂×C₉×C₁₁
Hall	C₂×C₁₁×C₁₉ ⋊ C₉
Hall	C₁₁×C₁₉ ⋊ C₂×C₉
Hall	C₂×C₁₉ ⋊ C₉×C₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₁	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₂×C₉×C₁₁
Frattini	C₃	C₂×C₁₁×C₁₉⋊C₃
Fitting, socle, prime radical	C₂×C₃×C₁₁×C₁₉	C₃
cosocle	C₃×C₁₉	C₂×C₃×C₁₁
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₃×C₁₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 3762

A minimal faithful permutation representation — 2 generators on 41 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13)(15,16,18)(17,20,21)(19,23,22)(24,28,26)(25,29,27)(30,32,31)(33,34,36,35,37,39,38,40,41);(14,15,17,21,26,31,28,16,19,24,29,18,22,27,20,25,30,32,23)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₅×C₁₁×#4294, C₂×C₁₁⋊C₅×#4294, D₅×C₁₁×#4294, …
maximal normal subgroup of	C₂×C₅×C₁₁×#4294, C₂×C₁₁⋊C₅×#4294, C₂×C₇×C₁₁×#4294
maximal quotient of	C₂×C₅×C₁₁×#4294, D₅×C₁₁×#4294, C₂×C₇×C₁₁×#4294, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3762, 5);

C2×C11×#4294 #16836765