C₁₉×#3028 #14560885

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3026
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#3028

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
prime radical	C₁₉×#585	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

716 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 212 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 — 4 generators on 51 points:

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

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#13351, C₁₉×#13352, C₁₉×#13354, …
maximal normal subgroup of	C₁₉×#13351, C₁₉×#13352, C₁₉×#13354, …
maximal quotient of	C₁₉×#18308, C₁₉×#18309, C₁₉×#18310, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1760);