C₁₇×C₈₁ #13063375

order	1377
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₁₆×C₂₇ (order 864) · Inn(G) = C₁ · Out(G) = C₂×C₁₆×C₂₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₃₇₇
abelian	C₁₇×C₈₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₇	C₃×C₁₇
socle, prime radical	C₃×C₁₇	C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

10 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 98
transitive degree	μ_t(G) = 1377

A minimal faithful permutation representation — 1 generator on 98 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)(82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98)

Conjugacy classes & character table

1377 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₇×C₂₄₃, C₃×C₁₇×C₈₁, C₁₇×C₈₁⋊C₃, …
maximal normal subgroup of	C₁₇×C₂₄₃, C₃×C₁₇×C₈₁, C₁₇×C₈₁⋊C₃, …
maximal quotient of	C₁₇×C₂₄₃, C₃×C₁₇×C₈₁, C₂×C₁₇×C₈₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1377, 1);

C17×C81 #13063375