C₁₇×#7070 #16864814

order	4352
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7070

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#102
commutator	C₈	C₂×C₁₆×C₁₇
Frattini, cosocle	C₈²	C₂²×C₁₇
socle	C₂²×C₁₇	D₄⋊C₈
prime radical	C₂×D₈×C₁₇	C₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₈²×C₁₇ ◁ G

156 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 66 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 — 2 generators on 49 points:

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

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 58);