C₅×C₁₉×Dic₁₁ #16862012

order	4180
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×C₁₉×Dic₁₁

Splittings

derived, Sylow	C₁₁ ⋊ C₄×C₅×C₁₉
Hall	C₅×C₁₁×C₁₉ ⋊ C₄
Hall	C₁₁×C₁₉ ⋊ C₄×C₅
Hall	C₅×C₁₁ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₉	D₁₁
commutator, hypocenter	C₁₁	C₄×C₅×C₁₉
Frattini	C₂	C₅×C₁₉×D₁₁
Fitting, socle, prime radical	C₂×C₅×C₁₁×C₁₉	C₂
cosocle	C₂×C₁₁	C₂×C₅×C₁₉
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₅×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 4180

A minimal faithful permutation representation — 2 generators on 39 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)(29,30,31,32,33,34,35,36,37,38,39);(25,27,26,28)(30,39)(31,38)(32,37)(33,36)(34,35)

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₅×C₁₉×Dic₁₁, C₅×C₁₉×Dic₃₃, C₅×Dic₁₁×C₁₉⋊C₃, …
maximal normal subgroup of	C₃×C₅×C₁₉×Dic₁₁, C₅×Dic₁₁×C₁₉⋊C₃, C₁₉×C₂₅×Dic₁₁, …
maximal quotient of	C₃×C₅×C₁₉×Dic₁₁, C₅×C₁₉×Dic₃₃, C₁₉×C₂₅×Dic₁₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4180, 4);

C5×C19×Dic11 #16862012