C₁₇×#7427 #16865171

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7426
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7427

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1351
commutator	C₂×C₂²⋊C₄	C₂×C₄×C₁₇
Frattini, cosocle	#381	C₂²×C₁₇
prime radical	C₂⁴×C₁₇	C₂²⋊C₄
LCS	G ▷ C₂×C₂²⋊C₄ ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂³×C₁₇ ◁ C₂⁴×C₁₇ ◁ C₁₇×#381 ◁ G

214 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 42 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 — 2 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,26,23,27,36,43)(20,28,30,44,31,45,47,49)(21,32,34,48,35,25,40,41)(24,37,38,29,39,46,42,33);(18,20)(19,24)(21,33,35,29)(22,30)(23,31)(25,28,32,45)(26,42)(27,39)(34,46,40,37)(36,47)(38,43)(41,44,48,49)

Conjugacy classes & character table

425 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 415);