C₁₇×#7385 #16865129

order	4352
nilpotency class	5
isoclinism	isoclinic class of #1418
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7385

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#357
commutator	C₁₆	C₂×C₈×C₁₇
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₇
prime radical	C₂×C₁₇×D₁₆	C₄
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₄×C₁₆×C₁₇ ◁ G

136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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) = 57
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 2 generators on 57 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,22,21,23,24,25)(26,27,29,35,31,37,32,48)(28,38,41,55,43,33,44,49)(30,45,40,52,47,53,46,36)(34,51,50,39,54,57,56,42);(27,33)(28,39)(29,32)(30,46)(34,52)(35,55)(36,54)(37,38)(40,47)(41,51)(42,43)(44,57)(45,50)(48,49)(53,56)

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, 373);