C₁₇×#7452 #16865196

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7418
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₇×#7452

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₇	#357
commutator	C₂×C₁₆	C₂×C₄×C₁₇
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₇
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₄×C₁₆×C₁₇ ◁ G

102 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 57
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 2 generators on 57 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(20,24)(23,25)(26,27,30,35,45,42,54,55,33,37,50,49,34,40,47,53,31,36,29,43,46,52,57,56,51,41,48,44,32,28,38,39);(18,19,21,23)(20,25,24,22)(26,28,31,40)(27,34,36,32)(29,44,30,49)(33,52,51,42)(35,48,43,50)(37,45,41,46)(38,53,47,39)(54,55,57,56)

Conjugacy classes & character table

833 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 440);