C₁₉×#1817 #14559674

order	2432
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#1817

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂³
commutator	C₂²	C₂²×C₈×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂³×C₁₉	C₂²×C₄
prime radical	C₂⁴×C₁₉	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

380 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 160 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 — 3 generators on 39 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)(26,29)(27,28)(30,31)(32,33,34,36,35,37,38,39);(25,28)(29,31);(21,23)(24,26,27,30)(25,29,28,31)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₉×#7017, C₁₉×#7021, C₁₉×#7033, …
maximal normal subgroup of	C₁₉×#7017, C₁₉×#7021, C₁₉×#7033, …
maximal quotient of	C₁₉×#8698, C₁₉×#8699, C₁₉×#8700, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 549);