C₁₇×#11421 #16869165

order	4352
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#11421

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₁₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
socle	C₂²×C₁₇	C₂×C₂²⋊C₈
prime radical	C₂²×#41×C₁₇	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂³×C₈×C₁₇ ◁ G

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

normal subgroups only

This group has 522 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)(20,24,25,22)(21,23)(26,27,30,36,31,37,45,54,32,34,46,50,29,35,43,52)(28,38,40,55,39,48,56,53,41,51,44,57,42,33,47,49);(18,20)(19,22)(21,25)(23,24)(26,28)(27,33)(29,42)(30,44)(31,39)(32,41)(34,48)(35,51)(36,53)(37,38)(40,46)(43,56)(45,47)(49,50)(52,55)(54,57);(27,34)(33,48)(35,37)(36,50)(38,51)(49,53)(52,54)(55,57)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4409);