C₁₉×#7120 #18013079

order	4864
nilpotency class	4
isoclinism	isoclinic class of #1347
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7120

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	#102
commutator	C₂×C₈	C₂×C₈×C₁₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₉
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

222 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 4864

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

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, 108);