C₂×C₉×C₂₉×C₃₇ #34064529

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

Aliases

cyclic	C₁₉₃₁₄
abelian	C₂×C₉×C₂₉×C₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₂₉×C₃₇
socle, prime radical	C₂×C₃×C₂₉×C₃₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 19314

A minimal faithful permutation representation — 1 generator on 77 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)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77)

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	C₉×C₂₉×Dic₃₇, C₉×C₃₇×Dic₂₉, C₉×Dic₁₀₇₃, …
maximal subgroup of	C₄×C₉×C₂₉×C₃₇, C₉×C₂₉×Dic₃₇, C₉×C₃₇×Dic₂₉, …
maximal normal subgroup of	C₄×C₉×C₂₉×C₃₇, C₉×C₂₉×Dic₃₇, C₉×C₃₇×Dic₂₉, …
maximal quotient of	C₄×C₉×C₂₉×C₃₇, C₂²×C₉×C₂₉×C₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19314, 1);

C2×C9×C29×C37 #34064529