C₁₇×#7448 #16865192

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7447
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7448

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1361
commutator	C₂×C₁₆	C₂×C₄×C₁₇
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₇
prime radical	C₁₇×#2246	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₄×C₁₆×C₁₇ ◁ G

146 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 544

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)(18,19,21,27,37,30,39,46,24,31,38,29,23,40,22,28)(20,32,34,26,45,44,49,43,36,47,48,42,35,25,33,41);(19,25)(20,33)(21,22)(23,37)(26,29)(27,42)(28,41)(30,47)(31,44)(32,40)(34,35)(36,49)(38,39)(43,46)(45,48)

Conjugacy classes & character table

629 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 436);