C₁₇×#12771 #16870515

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12767
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#12771

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1790
commutator	C₂×D₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×#41	C₂³×C₁₇
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×#41×C₁₇ ◁ G

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

normal subgroups only

This group has 728 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)(18,19,23,29,24,28,38,45)(20,26,31,43,21,32,34,46)(22,27,36,44,35,40,37,47)(25,39,41,33,42,48,49,30);(18,20,24,21)(19,25,28,42)(22,30,35,33)(23,34,38,31)(26,40,32,27)(29,41,45,49)(36,48,37,39)(43,47,46,44);(18,21,24,20)(19,26,28,32)(22,30,35,33)(23,31,38,34)(25,40,42,27)(29,46,45,43)(36,48,37,39)(41,44,49,47)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5759);