C₉×C₁₉×C₂₇ #17987249

order	4617
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 157464
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₉

Aliases

abelian

C₉×C₁₉×C₂₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₉	C₃²×C₁₉
socle, prime radical	C₃²×C₁₉	C₃×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 4617

A minimal faithful permutation representation — 2 generators on 55 points:

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

Conjugacy classes & character table

4617 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₂₇×#10587018, #28353143, #28353144, …
maximal subgroup of	C₁₉×C₂₇², C₁₉×#10624443, C₉×C₁₉×C₈₁, …
maximal normal subgroup of	C₁₉×C₂₇², C₁₉×#10624443, C₉×C₁₉×C₈₁, …
maximal quotient of	C₁₉×C₂₇², C₁₉×#10624443, C₁₉×#10624463, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 10);

C9×C19×C27 #17987249