C₁₉×C₂₃⋊D₂₃ #34117317

order	20102
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉ · Schur multiplier (H₂) = C₂₃

Aliases

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

Splittings

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

Subgroups

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

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 10051

A minimal faithful permutation representation — 3 generators on 65 points:

(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);(1,2,4,6,8,10,12,14,16,18,20,22,23,21,19,17,15,13,11,9,7,5,3)

Conjugacy classes & character table

5054 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20102, 7);

C19×C23⋊D23 #34117317