C₁₁×C₁₉×D₃₁ #27188367

order	12958
isoclinism	isoclinic class of D₃₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×C₁₉×D₃₁
unambiguous semidirect product	C₃₁⋊(C₂×C₁₁×C₁₉)

Splittings

Fitting, socle, Hall	C₁₁×C₁₉×C₃₁ ⋊ C₂
derived, Sylow	C₃₁ ⋊ C₂×C₁₁×C₁₉
Hall	C₁₉×C₃₁ ⋊ C₂×C₁₁
Hall	C₁₁×C₃₁ ⋊ C₂×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₁×C₁₉	D₃₁
commutator, cosocle, hypocenter	C₃₁	C₂×C₁₁×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₉×C₃₁	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₁₁×C₁₉

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 6479

A minimal faithful permutation representation — 2 generators on 61 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)(28,29)(30,31)(32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50)(51,52,53,54,55,56,57,58,59,60,61);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)

Conjugacy classes & character table

3553 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₁×D₁₉×D₃₁, C₁₉×D₁₁×D₃₁, D₃₁×D₂₀₉, …
maximal normal subgroup of	C₁₁×D₁₉×D₃₁, C₁₉×D₁₁×D₃₁, D₃₁×D₂₀₉, …
maximal quotient of	C₁₁×C₁₉×Dic₃₁, C₂×C₁₁×C₁₉×D₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12958, 2);

C11×C19×D31 #27188367