C₂×C₃²×C₂₉×C₃₇ #34064541

order	19314
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

abelian

C₂×C₃²×C₂₉×C₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 74
transitive degree	μ_t(G) = 19314

A minimal faithful permutation representation — 2 generators on 74 points:

(1,2)(3,4,5)(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)(38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74);(6,7,8)

Conjugacy classes & character table

19314 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₃⋊Dic₃₂₁₉, C₃₇×C₃⋊Dic₈₇, C₂₉×C₃⋊Dic₁₁₁, …
socle of	C₃²×C₄×C₂₉×C₃₇, C₃⋊Dic₃₂₁₉, C₃₇×C₃⋊Dic₈₇, …
maximal subgroup of	C₃²×C₄×C₂₉×C₃₇, C₃⋊Dic₃₂₁₉, C₃₇×C₃⋊Dic₈₇, …
maximal normal subgroup of	C₃²×C₄×C₂₉×C₃₇, C₃⋊Dic₃₂₁₉, C₃₇×C₃⋊Dic₈₇, …
maximal quotient of	C₃²×C₄×C₂₉×C₃₇, C₂²×C₃²×C₂₉×C₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19314, 13);

C2×C32×C29×C37 #34064541