C₁₇×#7125 #16864869

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7125

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#327
commutator	C₂×C₈	C₂×C₈×C₁₇
Frattini, cosocle	C₂×#97	C₂²×C₁₇
socle	C₂×C₁₇	#1271
prime radical	C₂³×C₁₇	#104
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#97 ◁ G

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

normal subgroups only

This group has 182 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) = 49
transitive degree	μ_t(G) = 544

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

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 113);