C₁₇×#733 #13063384

order	1377
nilpotency class	3
isoclinism	isoclinic class of AΣL(1,𝔽₂₇)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₇ · Schur multiplier (H₂) = C₃

Aliases

direct product

C₁₇×#733

Subgroups

	subgroup	G/H
center, socle	C₃×C₁₇	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃²	C₃²×C₁₇
prime radical	C₃²×C₁₇	C₃²
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₇ ◁ C₃²×C₁₇ ◁ G

26 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)(18,19,22,21,25,31,29,24,35)(20,26,30,28,23,32,39,34,42)(27,37,40,38,36,41,44,33,43);(18,20,27,29,39,44,21,28,38)(19,23,33,24,26,36,25,34,37)(22,30,40,35,42,43,31,32,41)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₇×#6878, C₁₇×#6880, C₁₇×#6881, …
maximal normal subgroup of	C₁₇×#6878, C₁₇×#6880, C₁₇×#6881, …
maximal quotient of	C₁₇×#6858, C₁₇×#6860, C₁₇×#6861, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1377, 10);

C17×#733 #13063384