C₄×C₁₁²×C₃₁ #28418477

order	15004
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁₁

Aliases

abelian

C₄×C₁₁²×C₃₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₁₁²×C₃₁
socle, prime radical	C₂×C₁₁²×C₃₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 15004

A minimal faithful permutation representation — 2 generators on 57 points:

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

Conjugacy classes & character table

15004 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₈×C₁₁²×C₃₁, C₂×C₄×C₁₁²×C₃₁
maximal normal subgroup of	C₈×C₁₁²×C₃₁, C₂×C₄×C₁₁²×C₃₁
maximal quotient of	C₈×C₁₁²×C₃₁, C₂×C₄×C₁₁²×C₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15004, 10);

C4×C112×C31 #28418477