C₁₉×#7184 #18013143

order	4864
nilpotency class	3
isoclinism	isoclinic class of #1284
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7184

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	#95
commutator	C₂×C₄	C₄×C₈×C₁₉
Frattini, cosocle	C₂³×C₈	C₂²×C₁₉
socle	C₂²×C₁₉	#336
prime radical	C₂⁴×C₁₉	M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₈×C₁₉ ◁ G

370 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 608

A minimal faithful permutation representation — 2 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)(22,26,27,24)(23,25)(28,29,31,36,33,35,40,42,32,37,39,43,30,34,38,41);(20,22)(21,24)(23,27)(25,26)(29,34,37,35)(36,41,43,42)

Conjugacy classes & character table

1216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 172);