C₁₉×C₂₃×D₂₃ #34117316

order	20102
isoclinism	isoclinic class of D₂₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×C₂₃×D₂₃
unambiguous semidirect product	C₂₃⋊(C₂×C₁₉×C₂₃)

Splittings

Fitting, socle, Hall	C₁₉×C₂₃² ⋊ C₂
derived	C₂₃ ⋊ C₂×C₁₉×C₂₃
Sylow	C₂₃² ⋊ C₂×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₂₃	D₂₃
commutator, cosocle, hypocenter	C₂₃	C₂×C₁₉×C₂₃
Frattini	C₁	G
Fitting, socle	C₁₉×C₂₃²	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₁₉×C₂₃

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 874

A minimal faithful permutation representation — 2 generators on 65 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(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);(24,25,27,29,31,33,35,37,39,41,43,45,46,44,42,40,38,36,34,32,30,28,26)

Conjugacy classes & character table

5681 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20102, 6);

C19×C23×D23 #34117316