C₁₉×C₂₉×C₄₉ #41008835

order	26999
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₆₉₉₉
abelian	C₁₉×C₂₉×C₄₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇	C₇×C₁₉×C₂₉
socle, prime radical	C₇×C₁₉×C₂₉	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 97
transitive degree	μ_t(G) = 26999

A minimal faithful permutation representation — 1 generator on 97 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)(69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97)

Conjugacy classes & character table

26999 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₂₆₉₉₉
Fitting subgroup of	D₂₆₉₉₉
maximal subgroup of	D₂₆₉₉₉
maximal normal subgroup of	D₂₆₉₉₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26999, 1);

C19×C29×C49 #41008835