C₁₇×#7422 #16865166

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7422
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#7422

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1347
commutator	C₂×C₁₆	C₂×C₄×C₁₇
Frattini, cosocle	C₂×M₃₂	C₂²×C₁₇
prime radical	C₁₇×#2218	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ C₂×C₁₇×M₃₂ ◁ G

150 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 46 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 — 2 generators on 49 points:

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

Conjugacy classes & character table

527 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 410);