C₁₇×#12287 #16870031

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12108
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#12287

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₁₇×#3203	C₂
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#408 ◁ G

318 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 74 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)(18,19,22,25)(20,23,27,30)(21,24,28,31)(26,32,33,29)(34,35)(36,48)(37,51)(38,54)(39,46)(40,45)(41,47)(42,49)(43,53)(44,57)(50,62)(52,61)(55,64)(56,59)(58,63)(60,65);(18,20)(19,23)(21,26)(22,27)(24,29)(25,30)(28,33)(31,32)(34,36,41,37)(35,42,47,61)(38,55,58,65)(39,50,40,53)(43,59,62,44)(45,60,46,64)(48,63,51,54)(49,56,52,57);(18,21)(19,24)(20,26)(22,28)(23,29)(25,31)(27,33)(30,32)(34,37,41,36)(35,43,47,62)(38,52,58,49)(39,50,40,53)(42,59,61,44)(45,48,46,51)(54,60,63,64)(55,57,65,56)

Conjugacy classes & character table

527 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5275);