C₁₇×#9014 #16866758

order	4352
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#9014

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	#120
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₂⁴×C₁₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

756 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 150 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) = 45
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 45 points:

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

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 2002);