C₁₇×#7166 #16864910

order	4352
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7166

Subgroups

	subgroup	G/H
center	C₄²×C₁₇	C₂²⋊C₄
commutator	C₂×C₄	C₄×C₈×C₁₇
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₇
socle	C₂²×C₁₇	#336
prime radical	C₂³×C₁₇	C₄⋊C₈
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

216 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 41
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 2 generators on 41 points:

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

Conjugacy classes & character table

1292 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 154);