C₂²×C₁₉×#108 #14560771

order	2432
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂²×C₁₉×#108

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₉	D₄
commutator	C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₄⋊C₄
prime radical	C₂⁴×C₁₉	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

480 conjugacy classes of subgroups; only the 360 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 360 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) = 39
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 39 points:

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

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#10859, C₁₉×#10860, C₁₉×#10864, …
maximal normal subgroup of	C₁₉×#10859, C₁₉×#10860, C₁₉×#10864, …
maximal quotient of	C₂²×C₁₉×#334, C₂²×C₁₉×#335, C₂×C₁₉×#1564, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1646);