C₁₇×#7386 #16865130

order	4352
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7386

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₇	#357
commutator	C₁₆	C₂×C₈×C₁₇
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₇
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₄×C₁₆×C₁₇ ◁ G

124 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 2 generators on 57 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,22,21,23,24,25)(27,32,33,47)(28,36)(29,41)(30,43)(34,51,50,56)(35,52,45,49)(37,42,48,46)(38,44)(39,57)(40,55)(53,54);(26,27,31,33)(28,37,40,48)(29,42,44,46)(30,45,43,35)(32,36,47,55)(34,38,50,41)(39,51,53,56)(49,57,52,54)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 374);