C₁₉×#12692 #18018651

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11502
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#12692

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#99
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×D₄	C₂³×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

976 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 976 conjugacy classes of subgroups — too many to draw. Only its 150 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) = 55
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 55 points:

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

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5680);