C₁₇×#7072 #16864816

order	4352
nilpotency class	4
isoclinism	isoclinic class of #1347
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7072

Subgroups

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

146 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 62 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)(20,23)(21,30)(22,26)(24,27)(25,28)(29,32)(31,33)(34,35,36,40,38,41,43,47,37,39,42,45,44,46,48,49);(19,23)(20,27)(21,28)(24,25)(26,32)(29,33)(30,31)(35,39)(36,42)(41,46)(43,48)

Conjugacy classes & character table

986 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 60);