C₁₇×#10024 #16867768

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#10024

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂²×D₄×C₁₇	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

512 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 98 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 — 3 generators on 49 points:

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

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, 3012);