C₁₇×#11458 #16869202

order	4352
nilpotency class	4
isoclinism	isoclinic class of #2121
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#11458

Subgroups

	subgroup	G/H
center	C₄×C₁₇	C₂×#99
commutator	C₂³	C₂²×C₈×C₁₇
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₇
socle	C₂×C₁₇	C₂×#324
prime radical	C₂⁴×C₁₇	C₂×C₈
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×M₁₆×C₁₇ ◁ G

364 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 138 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 — 3 generators on 49 points:

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

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4446);