C₁₇×#19618 #16877362

order	4352
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₇×#19618

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
socle	C₂²×C₁₇	C₂×#127
prime radical	C₂³×C₁₇	#127
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

690 conjugacy classes of subgroups; only the 278 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 278 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 — 4 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)(21,25)(22,31)(23,26)(24,30)(28,33)(29,32)(34,35,38,41)(36,42,45,49)(37,46,43,40)(39,47,48,44);(18,20,22,30,23,28,21,29)(19,24,25,27,26,32,31,33);(20,28)(24,32)(27,33)(29,30)(34,36,43,47,38,45,37,44)(35,39,46,49,41,48,40,42);(18,21,23,22)(19,25,26,31)(20,29,28,30)(24,27,32,33)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 12606);