C₁₇×#13827 #16871571

order	4352
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₁₇ · Schur multiplier (H₂) = C₂³×C₄³

Aliases

direct product

C₁₇×#13827

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₇	C₂⁴
commutator	C₂²	C₂²×C₄²×C₁₇
Frattini, cosocle	C₂⁴	C₂⁴×C₁₇
prime radical	C₂⁶×C₁₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₇ ◁ G

2878 conjugacy classes of subgroups; only the 622 normal subgroups are shown.

normal subgroups only

This group has 2878 conjugacy classes of subgroups — too many to draw. Only its 622 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) = 1088

A minimal faithful permutation representation — 4 generators on 41 points:

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

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, 6815);