C₁₇×#7018 #16864762

order	4352
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#7018

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	#95
commutator	C₂×C₄	C₄×C₈×C₁₇
Frattini, cosocle	C₄³	C₂²×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₄³×C₁₇ ◁ G

294 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 49
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 2 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,23)(20,21)(24,25)(26,27,28,30,29,31,32,33)(34,35)(36,42,44,48)(37,40)(38,41)(39,43,46,49)(45,47);(18,19,21,24,22,25,20,23)(34,36)(35,39,41,46)(37,43)(38,44)(40,42,47,48)(45,49)

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6);