C₁₉×#2213 #14560070

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

Aliases

direct product

C₁₉×#2213

Subgroups

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

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

normal subgroups only

This group has 170 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) = 35
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12310, C₁₉×#12311, C₁₉×#12314, …
maximal normal subgroup of	C₁₉×#12310, C₁₉×#12311, C₁₉×#12314, …
maximal quotient of	C₁₉×#12418, C₁₉×#12419, C₁₉×#12424, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 945);