C₁₇×#11838 #16869582

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11836
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#11838

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1514
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₇
prime radical	C₂³×C₁₇	AGL(1,ℤ/8)
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×M₁₆×C₁₇ ◁ G

280 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 90 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)(20,29)(21,33,35,43)(22,25)(23,28)(24,30,40,48)(26,37,44,47)(27,36)(31,45)(32,46)(34,39,49,41)(38,42);(18,20,23,32)(19,24,28,40)(21,34,35,49)(22,38,36,31)(25,39,27,41)(26,42,44,45)(29,33,46,43)(30,47,48,37);(19,25,28,27)(21,35)(24,39,40,41)(26,43,44,33)(29,45,46,42)(30,48)(34,49)(37,47)

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4826);