C₅×#6864 #11925937

order	1215
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₅×C₉² · Schur multiplier (H₂) = C₃

Aliases

direct product

C₅×#6864

Subgroups

	subgroup	G/H
center	C₃×C₅×C₉	C₃²
commutator	C₃	C₅×C₉²
Frattini, cosocle	C₃×C₉	C₃²×C₅
socle, prime radical	C₃²×C₅	C₃×C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₅×C₉ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 1215

A minimal faithful permutation representation — 2 generators on 41 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×#10624462, C₅×#10624500, C₅×#10624532, …
maximal normal subgroup of	C₅×#10624462, C₅×#10624500, C₅×#10624532, …
maximal quotient of	C₅×#10624443, C₅×#10624463, C₅×#10624500, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1215, 11);

C5×#6864 #11925937