C₁₉×#6855 #17987241

order	4617
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₉²×C₁₉ · Schur multiplier (H₂) = C₃³

Aliases

direct product

C₁₉×#6855

Subgroups

	subgroup	G/H
center, socle, prime radical	C₃³×C₁₉	C₃²
commutator	C₃	C₉²×C₁₉
Frattini, cosocle	C₃³	C₃²×C₁₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃³×C₁₉ ◁ G

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 4617

A minimal faithful permutation representation — 2 generators on 46 points:

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

Conjugacy classes & character table

1881 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#28353254, #28353260, #28353261, …
maximal subgroup of	C₁₉×#10624480, C₁₉×#10624481, C₁₉×#10624482, …
maximal normal subgroup of	C₁₉×#10624480, C₁₉×#10624481, C₁₉×#10624482, …
maximal quotient of	C₁₉×#10624463, C₁₉×H(3,ℤ/9), C₁₉×#10624465, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 2);

C19×#6855 #17987241