C₂²×C₁₇×#376 #16891731

order	4352
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄²×C₁₇ · Schur multiplier (H₂) = C₂⁸×C₄²

Aliases

direct product

C₂²×C₁₇×#376

Subgroups

	subgroup	G/H
center	C₂⁴×C₄×C₁₇	C₂²
commutator	C₂	C₂³×C₄²×C₁₇
Frattini, cosocle	C₂³	C₂⁵×C₁₇
socle, prime radical	C₂⁵×C₁₇	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄×C₁₇ ◁ G

5150 conjugacy classes of subgroups; only the 3614 normal subgroups are shown.

normal subgroups only

This group has 5150 conjugacy classes of subgroups — too many to draw. Only its 3614 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) = 37
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 5 generators on 37 points:

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

Conjugacy classes & character table

2720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 26975);