C₁₇×#12520 #16870264

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12506
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂×C₈

Aliases

direct product

C₁₇×#12520

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₁₇×#493	C₂²
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₈²×C₁₇ ◁ G

316 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 110 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)(19,22)(20,23)(24,25)(26,27,31,35)(28,36,38,50)(29,41,43,56)(30,44,42,34)(32,45,46,39)(33,48,49,37)(40,55,54,52)(47,53,51,57);(26,28,37,53,30,40,43,45,31,38,48,57,42,54,29,39)(27,32,41,52,34,47,49,50,35,46,56,55,44,51,33,36);(18,19,23,25,21,24,20,22)(28,38)(32,46)(36,50)(39,45)(40,54)(47,51)(52,55)(53,57)

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, 5508);