C₁₉×#11415 #18017374

order	4864
nilpotency class	2
isoclinism	isoclinic class of #7855
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#11415

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×C₄²
commutator	C₂×C₄	C₂×C₄²×C₁₉
Frattini, cosocle	C₄×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×#97
prime radical	C₂³×C₁₉	#97
LCS	G ▷ C₂×C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

246 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 158 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) = 2432

A minimal faithful permutation representation — 3 generators on 51 points:

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

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, 4403);