C₁₉×#13749 #18019708

order	4864
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄³×C₁₉ · Schur multiplier (H₂) = C₂²×C₄³

Aliases

direct product

C₁₉×#13749

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂	C₂×C₄³×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

2598 conjugacy classes of subgroups; only the 1374 normal subgroups are shown.

normal subgroups only

This group has 2598 conjugacy classes of subgroups — too many to draw. Only its 1374 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) = 39
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 4 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,27,26)(32,33,36,34)(35,38,39,37);(28,29,31,30)(33,34)(37,38);(20,21,22,23)(24,26,27,25)(28,30,31,29)(32,34,36,33)(35,38,39,37);(32,35)(33,37)(34,38)(36,39)

Conjugacy classes & character table

2584 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6737);