C₂³×C₁₇×SD₃₂ #16920370

order	4352
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₇ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂³×C₁₇×SD₃₂

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₇	D₈
commutator, Frattini, cosocle	C₈	C₂⁵×C₁₇
prime radical	C₂³×D₈×C₁₇	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ C₂³×C₈×C₁₇ ◁ G

2334 conjugacy classes of subgroups; only the 1054 normal subgroups are shown.

normal subgroups only

This group has 2334 conjugacy classes of subgroups — too many to draw. Only its 1054 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) = 39
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 5 generators on 39 points:

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

Conjugacy classes & character table

1496 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 55614);