C₁₉×#23357 #18029316

order	4864
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#23357

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂³×C₄
prime radical	C₂×C₁₉×#127	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

912 conjugacy classes of subgroups; only the 306 normal subgroups are shown.

normal subgroups only

This group has 912 conjugacy classes of subgroups — too many to draw. Only its 306 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) = 2432

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)(22,26)(23,27)(24,25)(28,29)(30,34)(31,33)(32,35)(36,37,40,43,39,41,38,42);(21,25)(22,23)(30,35)(32,34)(37,41)(42,43);(20,22,24,23)(21,26,25,27)(28,30,31,35)(29,32,33,34)(36,38,39,40)(37,42,41,43);(20,23,24,22)(21,26,25,27)(29,33)(32,34)(36,38,39,40)(37,42,41,43)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 16345);