C₁₉×#14170 #18020129

order	4864
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

direct product

C₁₉×#14170

Subgroups

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

1494 conjugacy classes of subgroups; only the 494 normal subgroups are shown.

normal subgroups only

This group has 1494 conjugacy classes of subgroups — too many to draw. Only its 494 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) = 4864

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

Conjugacy classes & character table

1444 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 7158);