C₁₇×#11428 #16869172

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#11428

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#99
commutator	C₂³	C₂²×C₈×C₁₇
Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₁₇
prime radical	C₂⁴×C₁₇	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#117 ◁ G

526 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 142 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)(18,19,20,22,21,23,24,25)(26,27)(28,36)(29,33)(30,43,44,34)(31,35)(32,38,46,53)(37,50)(39,51)(40,54)(41,56,57,48)(42,49)(45,52,47,55);(26,28,31,39)(27,32,35,46)(29,40,42,37)(30,38,44,53)(33,47,49,45)(34,36,43,51)(41,55,57,52)(48,54,56,50);(26,29,31,42)(27,33,35,49)(28,37,39,40)(30,41,44,57)(32,45,46,47)(34,48,43,56)(36,50,51,54)(38,52,53,55)

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, 4416);