C₁₇×#11497 #16869241

order	4352
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#11497

Subgroups

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

288 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 130 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) = 65
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 65 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26,28,23)(21,24)(22,25)(27,32,33,30)(29,31)(34,35,39,45,41,44,54,43,40,46,53,62,38,55,37,52)(36,47,50,63,49,42,57,59,51,61,65,58,56,60,48,64);(18,20,22,28)(19,23,25,26)(21,27,29,33)(24,30,31,32)(34,36,40,51)(35,42,46,60)(37,48,54,57)(38,56,41,49)(39,50,53,65)(43,58,52,63)(44,61,55,47)(45,59,62,64);(18,21,22,29)(19,24,25,31)(20,27,28,33)(23,30,26,32)(34,37,38,53,40,54,41,39)(35,43,55,45,46,52,44,62)(36,48,56,65,51,57,49,50)(42,58,47,59,60,63,61,64)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4485);