C₁₉×#3058 #14560915

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3057
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₉×#3058

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

524 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 608

A minimal faithful permutation representation — 4 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(25,29)(27,30)(31,35)(32,36)(34,37)(38,39);(24,25,30,36,28,32,27,29)(26,31,37,39,33,38,34,35);(21,23)(24,26)(25,31)(27,34)(28,33)(29,35)(30,37)(32,38)(36,39);(26,33)(31,38)(34,37)(35,39)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#11868, C₁₉×#11870, C₁₉×#13074, …
maximal normal subgroup of	C₁₉×#11868, C₁₉×#11870, C₁₉×#13074, …
maximal quotient of	C₁₉×#19187, C₁₉×#19192, C₁₉×#19198, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1790);