C₅×C₁₁×Dic₁₇ #16836660

order	3740
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×C₁₁×Dic₁₇

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₁	D₁₇
commutator, hypocenter	C₁₇	C₄×C₅×C₁₁
Frattini	C₂	C₅×C₁₁×D₁₇
Fitting, socle, prime radical	C₂×C₅×C₁₁×C₁₇	C₂
cosocle	C₂×C₁₇	C₂×C₅×C₁₁
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₅×C₁₁

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);(17,19,18,20)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₅×C₁₁×Dic₁₇, C₅×C₁₁×Dic₅₁, Dic₁₇×C₁₁⋊C₂₅, …
maximal normal subgroup of	C₃×C₅×C₁₁×Dic₁₇, Dic₁₇×C₁₁⋊C₂₅, C₁₁×C₂₅×Dic₁₇, …
maximal quotient of	C₃×C₅×C₁₁×Dic₁₇, C₅×C₁₁×Dic₅₁, C₁₁×C₂₅×Dic₁₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3740, 6);

C5×C11×Dic17 #16836660