C₁₇×#9157 #16866901

order	4352
nilpotency class	3
isoclinism	isoclinic class of #7694
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₇×#9157

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₂×C₁₇×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂²×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 648 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)(18,19)(20,21)(22,23,27,28,26,24,25,29)(30,31,34,37,35,38,33,43)(32,39,42,44,40,45,41,36);(22,24,26,23)(25,29,27,28)(30,32)(31,36,38,44)(33,41)(34,42)(35,40)(37,39,43,45);(19,21)(22,25,26,27)(23,28,24,29)(32,40)(36,44)(39,45)(41,42)

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, 2145);