C₁₇×#7058 #16864802

order	4352
nilpotency class	4
isoclinism	isoclinic class of #1343
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7058

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#99
commutator	C₂²×C₄	C₂×C₈×C₁₇
Frattini, cosocle	C₂×C₂²⋊C₈	C₂²×C₁₇
socle	C₂²×C₁₇	#323
prime radical	C₂²×#41×C₁₇	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×C₂²⋊C₈ ◁ G

354 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 54 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)(20,24,25,22)(21,23)(26,27,30,35,31,36,45,53,32,37,46,54,29,34,43,51)(28,38,40,55,39,49,56,52,41,50,44,57,42,33,47,48);(19,22)(23,24)(26,28)(27,33)(29,42)(30,44)(31,39)(32,41)(34,50)(35,52)(36,38)(37,49)(40,46)(43,56)(45,47)(48,54)(51,55)(53,57)

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 46);