C₂₃×D₄₃₇ #34117319

order	20102
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₃×D₄₃₇
unambiguous semidirect product	C₁₉⋊(C₂₃×D₂₃)
unambiguous semidirect product	C₂₃⋊(C₂₃×D₁₉)

Splittings

Fitting, socle, Hall	C₁₉×C₂₃² ⋊ C₂
derived	C₁₉×C₂₃ ⋊ C₂×C₂₃
Sylow	C₂₃² ⋊ D₁₉
Sylow	C₁₉ ⋊ C₂₃×D₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂₃	D₄₃₇
commutator, cosocle, hypocenter	C₁₉×C₂₃	C₂×C₂₃
Frattini	C₁	G
Fitting, socle	C₁₉×C₂₃²	C₂
LCS	G ▷ C₁₉×C₂₃
UCS	C₁ ◁ 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)(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)(47,48,50,52,54,56,58,60,62,64,65,63,61,59,57,55,53,51,49)

Conjugacy classes & character table

5060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20102, 9);

C23×D437 #34117319