C₁₇×#7081 #16864825

order	4352
nilpotency class	4
isoclinism	isoclinic class of #7076
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7081

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#327
commutator	C₂²×C₈	C₂×C₄×C₁₇
Frattini, cosocle	C₂×C₄⋊C₈	C₂²×C₁₇
prime radical	C₂³×C₁₇	#102
LCS	G ▷ C₂²×C₈ ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×C₄⋊C₈ ◁ G

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

normal subgroups only

This group has 172 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) = 49
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 2 generators on 49 points:

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

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, 69);