C₂₃²×D₁₉ #34117318

order	20102
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₃² · Schur multiplier (H₂) = C₂₃

Aliases

direct product	C₂₃²×D₁₉
unambiguous semidirect product	C₁₉⋊(C₂×C₂₃²)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂₃²	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂×C₂₃²
Frattini	C₁	G
Fitting, socle	C₁₉×C₂₃²	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂₃²

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 — 2 generators on 65 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65);(1,2,4,6,8,10,12,14,16,18,19,17,15,13,11,9,7,5,3)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42)

Conjugacy classes & character table

5819 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20102, 8);

C232×D19 #34117318