C₁₇×#12191 #16869935

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12148
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#12191

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₁₇
prime radical	C₁₇×#1595	C₂
LCS	G ▷ C₂×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₁₇ ◁ C₂×C₂²⋊C₄×C₁₇ ◁ G

484 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 544

A minimal faithful permutation representation — 3 generators on 41 points:

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

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5179);