C₃×C₁₉×#137 #14269815

order	1824
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃×C₁₉×#137

Subgroups

	subgroup	G/H
center, socle	C₂×C₃×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₄	C₂³×C₃×C₁₉
prime radical	C₃×#41×C₁₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₁₉ ◁ C₂×C₃×C₄×C₁₉ ◁ G

120 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 912

A minimal faithful permutation representation — 3 generators on 38 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)(25,31)(26,34)(27,29)(28,32)(30,36)(33,38)(35,37);(23,25,27,33)(24,28,29,37)(26,35,36,32)(30,38,34,31);(24,29)(28,37)(30,34)(31,38)

Conjugacy classes & character table

627 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1824, 1042);