C₁₇×#7528 #16865272

order	4352
nilpotency class	6
isoclinism	isoclinic class of #7527
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#7528

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1408
commutator	C₄×C₈	C₂×C₄×C₁₇
Frattini, cosocle	#492	C₂²×C₁₇
prime radical	C₁₇×#127	D₄
LCS	G ▷ C₄×C₈ ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄²×C₁₇ ◁ C₁₇×#492 ◁ G

142 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 30 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)(20,29,31,42)(21,33,35,25)(22,27,38,26)(23,28)(24,30,39,47)(32,46,37,45)(34,41)(36,43,49,44)(40,48);(18,20,23,32)(19,24,28,39)(21,34,36,48)(22,37,38,31)(25,42,44,45)(26,41,27,40)(29,33,46,43)(30,35,47,49)

Conjugacy classes & character table

323 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 516);