C₁₉×#11838 #18017797

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11836
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#11838

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1514
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
prime radical	C₂³×C₁₉	AGL(1,ℤ/8)
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×M₁₆×C₁₉ ◁ G

280 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 90 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)(22,31)(23,35,37,45)(24,27)(25,30)(26,32,42,50)(28,39,46,49)(29,38)(33,47)(34,48)(36,41,51,43)(40,44);(20,22,25,34)(21,26,30,42)(23,36,37,51)(24,40,38,33)(27,41,29,43)(28,44,46,47)(31,35,48,45)(32,49,50,39);(21,27,30,29)(23,37)(26,41,42,43)(28,45,46,35)(31,47,48,44)(32,50)(36,51)(39,49)

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4826);