C₁₇×#9007 #16866751

order	4352
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#9007

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#120
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
socle	C₂²×C₁₇	#386
prime radical	C₁₇×#3150	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

502 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 118 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 — 3 generators on 57 points:

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

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1995);