C₅×C₁₇×Dic₁₁ #16836661

order	3740
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×C₁₇×Dic₁₁

Splittings

derived, Sylow	C₁₁ ⋊ C₄×C₅×C₁₇
Hall	C₅×C₁₁×C₁₇ ⋊ C₄
Hall	C₁₁×C₁₇ ⋊ C₄×C₅
Hall	C₅×C₁₁ ⋊ C₄×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₇	D₁₁
commutator, hypocenter	C₁₁	C₄×C₅×C₁₇
Frattini	C₂	C₅×C₁₇×D₁₁
Fitting, socle, prime radical	C₂×C₅×C₁₁×C₁₇	C₂
cosocle	C₂×C₁₁	C₂×C₅×C₁₇
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₅×C₁₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 3740

A minimal faithful permutation representation — 2 generators on 37 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);(23,25,24,26)(28,37)(29,36)(30,35)(31,34)(32,33)

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₅×C₁₇×Dic₁₁, C₅×C₁₇×Dic₃₃, C₁₇×Dic₁₁⋊C₂₅, …
maximal normal subgroup of	C₃×C₅×C₁₇×Dic₁₁, C₁₇×Dic₁₁⋊C₂₅, C₁₇×C₂₅×Dic₁₁, …
maximal quotient of	C₃×C₅×C₁₇×Dic₁₁, C₅×C₁₇×Dic₃₃, C₁₇×C₂₅×Dic₁₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3740, 7);

C5×C17×Dic11 #16836661