C₁₉×#7415 #18013374

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7414
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7415

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1345
commutator	C₂×M₁₆	C₂×C₄×C₁₉
Frattini, cosocle	#423	C₂²×C₁₉
prime radical	C₁₉×#575	C₄
LCS	G ▷ C₂×M₁₆ ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#423 ◁ G

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

normal subgroups only

This group has 190 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)(22,30,32,42,34,46,33,49)(23,27,37,43)(24,39)(25,28)(26,31,40,47,41,48,45,35)(29,36)(38,51,50,44);(20,22)(21,26)(23,35)(24,32)(25,34)(27,42)(28,41)(29,45)(30,44)(31,38)(33,36)(37,47)(39,40)(43,49)(46,51)(48,50)

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, 403);