C₁₉×#12301 #18018260

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12301
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12301

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1613
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
prime radical	C₁₉×#3199	C₂
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ G

342 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 70 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)(20,21,24,40,25,30,41,29)(22,31,34,46,35,45,33,27)(23,36,38,28,39,26,37,43)(32,44,50,48,51,47,49,42);(21,26)(23,37)(24,41)(27,42)(28,40)(29,43)(30,36)(31,47)(32,49)(33,34)(38,39)(44,45)(46,48)(50,51);(20,22)(21,27)(23,32)(24,34)(25,35)(26,42)(28,47)(29,45)(30,46)(31,40)(33,41)(36,48)(37,49)(38,50)(39,51)(43,44)

Conjugacy classes & character table

475 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5289);