C₁₇×#11991 #16869735

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11989
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#11991

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1551
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₁₇×#540	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₁₇×#405 ◁ G

280 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 98 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)(18,19,21,27,34,24,33,37,23,28,36,43,22,26,35,42)(20,29,31,44,46,40,47,48,30,41,45,49,32,25,38,39);(19,24)(21,33)(22,34)(25,29)(26,28)(27,43)(31,47)(32,46)(35,36)(38,45)(39,48)(40,41);(18,20)(19,25,28,40)(21,31)(22,32)(23,30)(24,29,26,41)(27,39,43,48)(33,47)(34,46)(35,38)(36,45)(37,44,42,49)

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, 4979);