C₁₇×#10304 #16868048

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₇×#10304

Subgroups

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

934 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 934 conjugacy classes of subgroups — too many to draw. Only its 186 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) = 37
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(23,27)(24,25)(28,29)(30,31)(32,35)(33,36)(34,37);(19,21)(22,23)(24,28)(25,27)(26,29)(31,35)(32,33)(36,37);(23,27)(24,25)(28,29)(31,36)(32,33)(35,37)

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, 3292);