C₁₁×Dic₈₅ #16836664

order	3740
isoclinism	isoclinic class of D₈₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₁×Dic₈₅

Splittings

derived, Hall	C₅×C₁₇ ⋊ C₄×C₁₁
Hall	C₅×C₁₁×C₁₇ ⋊ C₄
Hall	C₁₁×C₁₇ ⋊ Dic₅
Hall	C₅×C₁₁ ⋊ Dic₁₇
Sylow	C₁₇ ⋊ C₁₁×Dic₅
Sylow	C₅ ⋊ C₁₁×Dic₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₈₅
commutator, hypocenter	C₅×C₁₇	C₄×C₁₁
Frattini	C₂	C₁₁×D₈₅
Fitting, socle, prime radical	C₂×C₅×C₁₁×C₁₇	C₂
cosocle	C₂×C₅×C₁₇	C₂×C₁₁
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₂×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);(12,14,13,15)(17,20)(18,19)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₁₁×Dic₈₅, C₁₁×Dic₂₅₅, C₁₁×Dic₄₂₅, …
maximal normal subgroup of	C₃×C₁₁×Dic₈₅, C₁₁⋊C₅×Dic₈₅, C₅×C₁₁×Dic₈₅, …
maximal quotient of	C₃×C₁₁×Dic₈₅, C₁₁×Dic₂₅₅, C₁₁×Dic₄₂₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3740, 10);

C11×Dic85 #16836664