C₁₉×#20773 #18026732

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

Aliases

direct product

C₁₉×#20773

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	C₂⁴×C₁₉	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

830 conjugacy classes of subgroups; only the 382 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 382 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 — 4 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)(22,27)(23,25)(24,26)(28,29)(30,32)(31,33)(34,35)(36,37,39,43,40,42,46,49)(38,41,45,48,44,47,50,51);(20,22,24,23)(21,25,26,27)(28,30,31,34)(29,32,33,35)(36,38)(37,41)(39,45)(40,44)(42,47)(43,48)(46,50)(49,51);(20,23,24,22)(21,25,26,27)(29,33)(32,35)(38,44)(41,47)(45,50)(48,51);(37,42)(41,47)(43,49)(48,51)

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, 13761);