C₁₇×#11456 #16869200

order	4352
nilpotency class	4
isoclinism	isoclinic class of #2127
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#11456

Subgroups

	subgroup	G/H
center	C₄×C₁₇	C₂×#99
commutator	C₂×C₄	C₂²×C₈×C₁₇
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₇
socle	C₂×C₁₇	C₂×#324
prime radical	C₂⁴×C₁₇	M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×M₁₆×C₁₇ ◁ G

364 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 138 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 — 3 generators on 49 points:

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

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, 4444);