C₁₇×#12201 #16869945

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12155
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#12201

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₇
prime radical	C₁₇×#537	C₂²
LCS	G ▷ C₂×C₄⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₁₇ ◁ C₂×C₄⋊C₄×C₁₇ ◁ G

380 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 1088

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

Conjugacy classes & character table

425 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5189);