C₁₇×#7702 #16865446

order	4352
nilpotency class	3
isoclinism	isoclinic class of #7694
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#7702

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₄³×C₁₇ ◁ G

410 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 4352

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

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, 690);