C₁₇×#7359 #16865103

order	4352
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#7359

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#354
commutator	C₄²	C₂×C₈×C₁₇
Frattini, cosocle	#382	C₂²×C₁₇
prime radical	C₂³×C₁₇	#99
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#382 ◁ G

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 1088

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)(26,27)(28,36,38,51)(29,40,42,56)(30,44,46,34)(31,35)(32,37,47,54)(33,43)(39,53,45,52)(41,48,55,49)(50,57);(26,28)(27,32,35,49)(29,41)(30,45)(31,39)(33,36,50,53)(34,47,44,48)(37,42)(38,46)(40,51,56,52)(43,55)(54,57)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 347);