C₁₉×#2212 #14560069

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2212
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#2212

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#459
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₁₉×#509	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

154 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,30)(23,35)(24,39)(25,41)(26,31)(27,33)(28,32)(29,40)(34,48)(36,47)(37,51)(38,43)(42,44)(45,49)(46,50);(20,22,24,33,26,34,40,25)(21,27,29,30,31,41,39,48)(23,32,36,49,38,50,37,42)(28,43,44,47,46,35,45,51);(20,23)(21,28)(22,32)(24,36)(25,42)(26,38)(27,43)(29,44)(30,47)(31,46)(33,49)(34,50)(35,41)(37,40)(39,45)(48,51)

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2212, C₁₉×#33594, C₁₉×#33595, …
maximal normal subgroup of	C₂×C₁₉×#2212, C₁₉×#33594, C₁₉×#33595, …
maximal quotient of	C₁₉×#12416, C₁₉×#12417, C₁₉×#12420, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 944);