C₂×C₅×C₄₁×C₄₇ #34064274

order	19270
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₉₂₇₀
abelian	C₂×C₅×C₄₁×C₄₇

Subgroups

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

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 19270

A minimal faithful permutation representation — 1 generator on 95 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)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95)

Conjugacy classes & character table

19270 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₅×C₄₁×Dic₄₇, C₅×C₄₇×Dic₄₁, C₅×Dic₁₉₂₇, …
socle of	C₄×C₅×C₄₁×C₄₇, C₅×C₄₁×Dic₄₇, C₅×C₄₇×Dic₄₁, …
maximal subgroup of	C₄×C₅×C₄₁×C₄₇, C₅×C₄₁×Dic₄₇, C₅×C₄₇×Dic₄₁, …
maximal normal subgroup of	C₄×C₅×C₄₁×C₄₇, C₅×C₄₁×Dic₄₇, C₅×C₄₇×Dic₄₁, …
maximal quotient of	C₄×C₅×C₄₁×C₄₇, C₂²×C₅×C₄₁×C₄₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19270, 1);

C2×C5×C41×C47 #34064274