C₁₇×#7400 #16865144

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7398
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7400

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1343
commutator	C₂²×C₈	C₂×C₄×C₁₇
Frattini, cosocle	#408	C₂²×C₁₇
prime radical	C₁₇×#2018	C₂
LCS	G ▷ C₂²×C₈ ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#408 ◁ G

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

normal subgroups only

This group has 254 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)(18,19,21,26,23,27,35,45)(20,29,32,43,33,25,40,42)(22,28,36,44,31,41,34,48)(24,37,38,30,39,46,49,47);(19,24)(20,30)(21,34)(22,31)(25,28)(26,43)(27,39)(29,41)(33,47)(35,36)(37,46)(38,44)(42,45)(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, 388);