C₁₇×#12363 #16870107

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12324
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#12363

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₇	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₁₇×#446 ◁ G

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

normal subgroups only

This group has 278 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) = 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)(19,23)(20,24)(21,25)(26,27,31,35)(28,36,38,55)(29,40,42,54)(30,45,43,34)(32,47,48,37)(33,50,52,44)(39,56,46,51)(41,53,57,49);(18,19,22,20)(21,24,25,23)(26,28,31,38)(27,32,35,48)(29,41,42,57)(30,46,43,39)(33,51,52,56)(34,53,45,49)(36,54,55,40)(37,50,47,44);(18,20,22,19)(21,23,25,24)(29,42)(33,52)(36,55)(37,47)(40,54)(41,57)(44,50)(51,56)

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, 5351);