C₁₉×#11770 #18017729

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11769
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#11770

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1505
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
prime radical	C₁₉×#3176	C₂
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#405 ◁ G

316 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 608

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)(22,27)(23,36,38,26)(24,29)(25,31)(28,37,40,47)(30,33)(32,42)(34,48,49,39)(35,44)(41,45,50,51)(43,46);(21,26)(22,32)(23,37)(24,33)(27,41)(28,30)(29,40)(31,36)(34,49)(35,46)(38,47)(39,42)(43,48)(44,50);(20,22,33,46,25,35,24,32)(21,27,30,43,31,44,29,42)(23,34,47,51,38,49,37,45)(26,39,40,50,36,48,28,41)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4758);