C₁₇×#13079 #16870823

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13077
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#13079

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1893
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₁₇×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#131 ◁ G

486 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 146 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)(18,19,24,27,23,29,40,28)(20,30,26,39,33,44,32,22)(21,25,36,42,35,43,37,46)(31,48,41,34,49,47,45,38);(18,20,22,19,24,32,30,28,23,33,39,29,40,26,44,27)(21,31,38,25,37,41,47,42,35,49,34,43,36,45,48,46);(18,21)(19,25)(20,31)(22,38)(23,35)(24,37)(26,45)(27,46)(28,42)(29,43)(30,47)(32,41)(33,49)(34,39)(36,40)(44,48)

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, 6067);