C₁₉×#2643 #14560500

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#2643

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

462 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 184 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) = 43
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 43 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2643, C₁₉×#34570, C₁₉×#34584, …
maximal normal subgroup of	C₂×C₁₉×#2643, C₁₉×#34570, C₁₉×#34584, …
maximal quotient of	C₁₉×#14259, C₁₉×#14265, C₁₉×#14331, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1375);