C₁₉×#7400 #18013359

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7398
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7400

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1343
commutator	C₂²×C₈	C₂×C₄×C₁₉
Frattini, cosocle	#408	C₂²×C₁₉
prime radical	C₁₉×#2018	C₂
LCS	G ▷ C₂²×C₈ ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#408 ◁ G

254 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 42 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 — 2 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,28,25,29,37,47)(22,31,34,45,35,27,42,44)(24,30,38,46,33,43,36,50)(26,39,40,32,41,48,51,49);(21,26)(22,32)(23,36)(24,33)(27,30)(28,45)(29,41)(31,43)(35,49)(37,38)(39,48)(40,46)(44,47)(50,51)

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, 388);