C₁₇×#12079 #16869823

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12077
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#12079

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₇	#442
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₁₇×#322 ◁ G

204 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 4352

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)(18,19,21,20,22,23,25,24)(26,27,30,34,32,36,31,47)(28,37,39,55,41,56,40,52)(29,42,45,54,44,53,46,35)(33,48,50,38,51,43,49,57);(26,28,32,41)(27,33,36,51)(29,43,44,48)(30,40,31,39)(34,49,47,50)(35,52,54,55)(37,42,56,53)(38,46,57,45);(18,20,21,23,22,24,25,19)(27,34,36,47)(29,44)(33,49,51,50)(35,53,54,42)(37,55,56,52)(38,57)(43,48)(45,46)

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, 5067);