C₁₇×#7481 #16865225

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7481
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#7481

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1390
commutator	C₂×Q₈	C₄²×C₁₇
Frattini, cosocle	C₂×#124	C₂²×C₁₇
prime radical	C₂²×D₄×C₁₇	D₄
LCS	G ▷ C₂×Q₈ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂³×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#124 ◁ G

284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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)(20,28,30,44)(21,33,34,43)(22,36,38,27)(23,26)(24,29,39,47)(25,35)(31,46,32,45)(37,42)(40,48,41,49);(18,20)(19,24,26,40)(21,29)(22,30)(23,32)(25,28,42,45)(27,39,36,41)(31,38)(33,44,43,46)(34,48)(35,49)(37,47)

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 469);