C₁₇×#7164 #16864908

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

Aliases

direct product

C₁₇×#7164

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#95
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 ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

212 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 106 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)(26,27,30,34,31,35,40,37,32,36,41,28,29,33,39,38);(19,22,24,23)(26,28,30,35,31,38,40,36,32,34,41,33,29,37,39,27)

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 152);