C₁₉×#12074 #18018033

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

Aliases

direct product

C₁₉×#12074

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₄×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₄×D₈
prime radical	C₂×D₈×C₁₉	C₂×C₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₈²×C₁₉ ◁ G

226 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 43
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22,24,25,27,26)(28,29)(30,35)(31,34)(32,41)(33,37)(36,39)(38,42)(40,43);(29,34)(30,32)(31,39)(35,36)(37,43)(38,40)(41,42);(20,22,23,25,24,26,27,21)(28,30,33,32)(29,35,37,41)(31,38,40,39)(34,42,43,36)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5062);