C₁₉×#12874 #18018833

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12873
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#12874

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1823
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

376 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 138 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)(20,21,24,31,26,29,25,41)(22,32,34,45,35,27,40,44)(23,36,38,46,39,28,37,30)(33,42,49,48,50,47,51,43);(20,22)(21,27)(23,33)(24,40)(25,34)(26,35)(28,42)(29,32)(30,43)(31,45)(36,47)(37,49)(38,51)(39,50)(41,44)(46,48);(21,28,29,36)(23,37)(24,25)(27,42,32,47)(30,31,46,41)(33,49)(34,40)(38,39)(43,45,48,44)(50,51)

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5862);