C₁₇×#13056 #16870800

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#13056

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	B(4,𝔽₂)
commutator	C₂×Q₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×Q₈	C₂³×C₁₇
prime radical	C₂×C₁₇×2₋¹⁺⁴	C₂²
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₁₇ ◁ C₂²×Q₈×C₁₇ ◁ G

632 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 53
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23,25,33,28,34,26,31)(24,35,38,29,39,46,36,47)(27,32,41,30,43,48,40,49)(37,50,51,53,42,44,52,45);(18,19,20,21)(22,24)(23,29)(25,36)(26,38)(27,42)(28,39)(30,44)(31,46)(32,45)(33,35)(34,47)(37,43)(40,52)(41,51)(48,53)(49,50);(22,25,28,26)(23,30,34,49)(24,36,39,38)(27,41,43,40)(29,44,47,50)(31,48,33,32)(35,45,46,53)(37,52,42,51)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6044);