C₁₉×#1545 #14559402

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#1545

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₄²	C₂³×C₁₉
prime radical	C₂×C₁₉×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

344 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 112 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) = 608

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)(20,21,22,25,23,24,26,27)(28,29)(30,32)(31,33)(34,35);(21,24)(22,26)(29,32)(30,35)(33,34);(21,24)(25,27)(29,33)(32,34)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8383, C₁₉×#8384, C₁₉×#8385, …
maximal normal subgroup of	C₁₉×#8383, C₁₉×#8384, C₁₉×#8385, …
maximal quotient of	C₁₉×#7572, C₁₉×#7587, C₁₉×#7606, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 277);