C₄×C₁₁×C₁₇×C₃₁ #37550840

order	23188
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₃₁₈₈
abelian	C₄×C₁₁×C₁₇×C₃₁
multiplicative	(ℤ/23189)ˣ, (ℤ/46378)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₁₁×C₁₇×C₃₁
socle, prime radical	C₂×C₁₁×C₁₇×C₃₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 23188

A minimal faithful permutation representation — 1 generator on 63 points:

(1,2,3,4)(5,6,7,8,9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63)

Conjugacy classes & character table

23188 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₁₅₉₄, D₂₃₁₈₈
maximal subgroup of	Dic₁₁₅₉₄, D₂₃₁₈₈
maximal normal subgroup of	Dic₁₁₅₉₄, D₂₃₁₈₈
automorphism group of	C₂₃₁₈₉
outer automorphism group of	C₂₃₁₈₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23188, 1);

C4×C11×C17×C31 #37550840