C₁₇×#12031 #16869775

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12028
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#12031

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#106
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₂³×C₁₇	#106
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

200 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 114 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)(18,19,21,24,22,25,28,31)(20,23,27,30,26,29,32,33)(34,35)(36,45,48,60)(37,42)(38,51)(39,54)(40,44)(41,47,56,63)(43,52)(46,59,49,61)(50,58)(53,65)(55,62,57,64);(18,20)(19,23)(21,27)(22,26)(24,30)(25,29)(28,32)(31,33)(34,36,38,47,39,46,52,62,40,48,53,63,37,49,50,64)(35,41,43,45,42,57,51,61,44,56,58,60,54,55,65,59);(20,26)(23,29)(27,32)(30,33)(34,37,40,39)(35,42,44,54)(36,46,48,49)(38,50,53,52)(41,55,56,57)(43,51,58,65)(45,59,60,61)(47,62,63,64)

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, 5019);