C₁₉×#2206 #14560063

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#2206

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

186 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 68 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)(21,23)(24,25)(26,29)(27,36)(28,32)(30,33)(31,34)(35,38)(37,39);(20,21,22,23);(25,29)(26,33)(27,34)(30,31)(32,38)(35,39)(36,37)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12316, C₁₉×#12319, C₁₉×#12324, …
maximal normal subgroup of	C₁₉×#12316, C₁₉×#12319, C₁₉×#12324, …
maximal quotient of	C₁₉×#12416, C₁₉×#12424, C₁₉×#12445, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 938);