C₂₃×Dic₄₁ #16836823

order	3772
isoclinism	isoclinic class of D₄₁
automorphism	?
homology	Abelianization (H₁) = C₄×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₂₃×Dic₄₁

Splittings

derived, Sylow	C₄₁ ⋊ C₄×C₂₃
Hall	C₂₃×C₄₁ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₃	D₄₁
commutator, hypocenter	C₄₁	C₄×C₂₃
Frattini	C₂	C₂₃×D₄₁
Fitting, socle, prime radical	C₂×C₂₃×C₄₁	C₂
cosocle	C₂×C₄₁	C₂×C₂₃
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂×C₂₃

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 68
transitive degree	μ_t(G) = 3772

A minimal faithful permutation representation — 2 generators on 68 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)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68);(24,26,25,27)(29,68)(30,67)(31,66)(32,65)(33,64)(34,63)(35,62)(36,61)(37,60)(38,59)(39,58)(40,57)(41,56)(42,55)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49)

Conjugacy classes & character table

1012 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₂₃×Dic₄₁, C₂₃×Dic₁₂₃, C₅×C₂₃×Dic₄₁, …
maximal normal subgroup of	C₃×C₂₃×Dic₄₁, C₅×C₂₃×Dic₄₁, C₂₃×Dic₄₁⋊C₅, …
maximal quotient of	C₃×C₂₃×Dic₄₁, C₂₃×Dic₁₂₃, C₅×C₂₃×Dic₄₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3772, 3);

C23×Dic41 #16836823