C₁₇×#7221 #16864965

order	4352
nilpotency class	4
isoclinism	isoclinic class of #7221
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#7221

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#340
commutator	C₂×C₈	C₄²×C₁₇
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₇
prime radical	C₂³×C₁₇	#102
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

206 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 90 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)(20,26,28,32)(21,24)(22,25)(23,27,30,33)(29,31)(34,35,38,42)(36,37,44,46)(39,41,47,49)(40,48,45,43);(18,20)(19,23,25,30)(21,27)(22,28)(24,26,31,32)(29,33)(34,36,39,43,40,41,46,42,38,44,47,48,45,49,37,35)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 209);