C₁₇×#14661 #16872405

order	4352
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵×C₄²

Aliases

direct product

C₁₇×#14661

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₇
Frattini, cosocle	C₂⁴	C₂⁴×C₁₇
prime radical	C₂²×C₁₇×#127	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₇ ◁ G

2502 conjugacy classes of subgroups; only the 462 normal subgroups are shown.

normal subgroups only

This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 462 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 — 4 generators on 41 points:

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

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 7649);