C₁₇×#7446 #16865190

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

Aliases

direct product

C₁₇×#7446

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#357
commutator	C₂×C₁₆	C₂×C₄×C₁₇
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₇
prime radical	C₂×C₁₇×D₁₆	C₄
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₄×C₁₆×C₁₇ ◁ G

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

normal subgroups only

This group has 136 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) = 2176

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)(18,19,20,23,21,22,24,25)(27,33,34,49)(28,38)(29,44)(30,40)(31,46)(35,52,36,53)(37,54,48,51)(39,45,50,47)(41,43)(42,57)(55,56);(19,22)(20,24)(26,27)(28,39)(29,45)(30,47)(31,48)(32,34)(33,41)(35,44)(36,40)(37,46)(38,49)(42,52)(43,50)(51,56)(53,55)(54,57)

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, 434);