C₁₇×#7145 #16864889

order	4352
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₆×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#7145

Subgroups

	subgroup	G/H
center	C₄²×C₁₇	C₄²
commutator	C₄	C₄×C₁₆×C₁₇
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₇
socle	C₂²×C₁₇	#336
prime radical	C₂³×C₁₇	C₄⋊C₈
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₇ ◁ G

222 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 2176

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)(18,19)(20,27,29,33)(21,25)(22,31)(23,26)(24,28,32,30)(34,35,36,39,37,40,42,45,38,41,43,46,44,47,48,49);(18,20,22,30,23,29,21,28)(19,24,25,27,26,32,31,33)

Conjugacy classes & character table

1496 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 133);