C₁₇×#12769 #16870513

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12767
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#12769

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1790
commutator	C₂×D₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×#41	C₂³×C₁₇
prime radical	C₁₇×#3549	C₂
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×#41×C₁₇ ◁ G

856 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 856 conjugacy classes of subgroups — too many to draw. Only its 138 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) = 33
transitive degree	μ_t(G) = 272

A minimal faithful permutation representation — 3 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,25,22,24,28,32)(20,23,27,31,26,30,29,33);(19,23)(21,28)(24,30)(25,31)(27,29)(32,33);(19,24)(20,26)(21,28)(23,30)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5757);