C₁₇×#12874 #16870618

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12873
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#12874

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1823
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₂×#41×C₁₇	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#131 ◁ G

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

normal subgroups only

This group has 376 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)(18,19,22,29,24,27,23,39)(20,30,32,43,33,25,38,42)(21,34,36,44,37,26,35,28)(31,40,47,46,48,45,49,41);(18,20)(19,25)(21,31)(22,38)(23,32)(24,33)(26,40)(27,30)(28,41)(29,43)(34,45)(35,47)(36,49)(37,48)(39,42)(44,46);(19,26,27,34)(21,35)(22,23)(25,40,30,45)(28,29,44,39)(31,47)(32,38)(36,37)(41,43,46,42)(48,49)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5862);