C₁₇×#11311 #16869055

order	4352
nilpotency class	3
isoclinism	isoclinic class of #2069
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#11311

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#396
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
socle	C₂×C₁₇	#1443
prime radical	C₂⁴×C₁₇	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

532 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 202 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) = 49
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 49 points:

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

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, 4299);