C₁₇×C₂₇⋊C₃ #13063380

order	1377
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃×C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×C₂₇⋊C₃
unambiguous semidirect product	C₂₇⋊(C₃×C₁₇)
unambiguous semidirect product	(C₁₇×C₂₇)⋊C₃

Subgroups

	subgroup	G/H
center	C₉×C₁₇	C₃²
commutator	C₃	C₃×C₉×C₁₇
Frattini, cosocle	C₉	C₃²×C₁₇
socle	C₃×C₁₇	C₃×C₉
prime radical	C₃²×C₁₇	C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉×C₁₇ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 459

A minimal faithful permutation representation — 2 generators on 44 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,20,24,30,26,33,38,21,25,29,27,34,37,35,41,43,28,23,31,36,32,39,42,40,44);(19,23,25)(22,29,31)(24,32,34)(30,37,39)(33,40,41)(38,43,44)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₇×#6869, C₁₇×#6872, C₁₇×#6873, …
maximal normal subgroup of	C₁₇×#6869, C₁₇×#6872, C₁₇×#6873, …
maximal quotient of	C₁₇×#6864, C₁₇×C₃²⋊C₂₇, C₁₇×C₉⋊C₂₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1377, 6);

C17×C27⋊C3 #13063380