C₁₇×#8139 #16865883

order	4352
nilpotency class	2
isoclinism	isoclinic class of #7855
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#8139

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂×C₄²
commutator	C₂×C₄	C₂×C₄²×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
socle	C₂²×C₁₇	#376
prime radical	C₂³×C₁₇	#117
LCS	G ▷ C₂×C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ G

330 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 174 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 — 3 generators on 57 points:

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

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1127);