C₁₉×#2250 #14560107

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2218
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#2250

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

198 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 72 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)(25,29)(26,30)(27,33)(31,35)(32,39)(34,38)(36,37);(24,25,30,37,27,32,34,35,28,31,38,39,33,36,26,29);(20,21,22,23)(25,31)(29,35)(32,36)(37,39)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12324, C₁₉×#12325, C₁₉×#12336, …
maximal normal subgroup of	C₁₉×#12324, C₁₉×#12325, C₁₉×#12336, …
maximal quotient of	C₁₉×#12506, C₁₉×#12508, C₁₉×#12512, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 982);