C₁₇×#13856 #16871600

order	4352
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₇×#13856

Subgroups

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

1774 conjugacy classes of subgroups; only the 734 normal subgroups are shown.

normal subgroups only

This group has 1774 conjugacy classes of subgroups — too many to draw. Only its 734 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) = 4352

A minimal faithful permutation representation — 4 generators on 37 points:

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

Conjugacy classes & character table

1496 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6844);