C₄×C₇×C₁₇×C₃₇ #31798541

order	17612
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₇₆₁₂
abelian	C₄×C₇×C₁₇×C₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₇×C₁₇×C₃₇
socle, prime radical	C₂×C₇×C₁₇×C₃₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 17612

A minimal faithful permutation representation — 1 generator on 65 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)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65)

Conjugacy classes & character table

17612 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₈₈₀₆, D₁₇₆₁₂
maximal subgroup of	Dic₈₈₀₆, D₁₇₆₁₂
maximal normal subgroup of	Dic₈₈₀₆, D₁₇₆₁₂

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17612, 1);

C4×C7×C17×C37 #31798541