C₁₇×C₂₃×C₄₉ #34062523

order	19159
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₉₁₅₉
abelian	C₁₇×C₂₃×C₄₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇	C₇×C₁₇×C₂₃
socle, prime radical	C₇×C₁₇×C₂₃	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 89
transitive degree	μ_t(G) = 19159

A minimal faithful permutation representation — 1 generator on 89 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)

Conjugacy classes & character table

19159 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₉₁₅₉
Fitting subgroup of	C₁₇×D₂₃×C₄₉, C₂₃×D₁₇×C₄₉, C₄₉×D₃₉₁, …
maximal subgroup of	C₂×C₁₇×C₂₃×C₄₉, C₁₇×D₂₃×C₄₉, C₂₃×D₁₇×C₄₉, …
maximal normal subgroup of	C₂×C₁₇×C₂₃×C₄₉, C₁₇×D₂₃×C₄₉, C₂₃×D₁₇×C₄₉, …
maximal quotient of	C₂×C₁₇×C₂₃×C₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19159, 1);

C17×C23×C49 #34062523