C₁₉×#12533 #18018492

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12525
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₉×#12533

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈²×C₁₉ ◁ G

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

normal subgroups only

This group has 238 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) = 67
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 3 generators on 67 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,27)(22,28,29,35)(23,31,32,26)(25,33,34,30)(36,37)(38,46)(39,42)(40,53)(41,54)(43,49)(44,47)(45,52)(48,58)(50,65)(51,66)(55,63)(56,62)(57,67)(59,61)(60,64);(20,22,23,30,24,29,32,33)(21,25,26,28,27,34,31,35)(37,42)(43,55)(44,56)(45,54)(46,58)(53,66)(57,59)(60,65);(22,29)(25,34)(28,35)(30,33)(36,38,47,61,41,50,51,63,39,48,62,67,52,64,40,49)(37,43,53,60,45,57,56,58,42,55,66,65,54,59,44,46)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5521);