C₁₇×#8133 #16865877

order	4352
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₁₇ · Schur multiplier (H₂) = C₂×C₄²

Aliases

direct product

C₁₇×#8133

Subgroups

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

446 conjugacy classes of subgroups; only the 270 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 270 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 — 3 generators on 49 points:

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

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1121);