C₁₇×#12508 #16870252

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12506
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#12508

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₁₇×#493	C₂²
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₈²×C₁₇ ◁ G

280 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 102 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 — 3 generators on 41 points:

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

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5496);