C₁₇×#7424 #16865168

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

Aliases

direct product

C₁₇×#7424

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

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

normal subgroups only

This group has 146 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)(18,19,21,27,24,30,37,29)(20,25,33,41,36,43,35,48)(22,39,32,28,23,40,38,47)(26,44,42,34,45,49,46,31);(19,25)(20,31)(21,37)(22,38)(23,32)(26,28)(27,41)(29,48)(30,43)(33,49)(34,36)(35,44)(39,46)(40,42)(45,47)

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, 412);