C₁₇×#12518 #16870262

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12503
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂×C₈

Aliases

direct product

C₁₇×#12518

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₁₇×#2246	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₈²×C₁₇ ◁ G

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

normal subgroups only

This group has 330 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)(28,36)(29,41)(30,33)(31,44)(32,38)(34,37)(35,42)(39,48)(40,55)(43,56)(45,54)(46,57)(47,52)(49,51)(50,53);(26,28,37,51,31,40,43,54,30,39,52,57,42,53,29,38)(27,32,41,50,35,46,47,48,33,45,56,55,44,49,34,36);(18,19,23,25,21,24,20,22)(27,33)(32,45)(34,47)(35,44)(36,48)(41,56)(46,49)(50,55)

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5506);