C₁₇×#12347 #16870091

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12316
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#12347

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₁₇×#3341	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₈×D₄×C₁₇ ◁ G

302 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 57
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 57 points:

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

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5335);