C₁₉×#12314 #18018273

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12314
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#12314

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1619
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

384 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 35
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,25)(22,29)(23,33)(26,34)(27,35)(28,31)(30,32);(22,30)(23,33)(25,34)(26,28)(29,32)(31,35);(20,21)(22,31)(23,26)(24,27)(25,29)(28,33)(30,35)(32,34)

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, 5302);