C₂²×C₁₇×#383 #16891752

order	4352
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄×C₁₇ · Schur multiplier (H₂) = C₂¹⁰

Aliases

direct product

C₂²×C₁₇×#383

Subgroups

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

3678 conjugacy classes of subgroups; only the 2078 normal subgroups are shown.

normal subgroups only

This group has 3678 conjugacy classes of subgroups — too many to draw. Only its 2078 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) = 4352

A minimal faithful permutation representation — 5 generators on 41 points:

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

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 26996);