C₁₇×#11536 #16869280

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11508
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#11536

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₇
prime radical	C₂³×C₁₇	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₄×Q₈×C₁₇ ◁ G

376 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 106 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)(18,19,21,23,22,24,20,25)(26,27)(28,36,39,51)(29,33)(30,43,45,34)(31,35)(32,38)(37,52,40,54)(41,56,57,49)(42,50)(44,47)(46,53)(48,55);(26,28,31,39)(27,32,35,47)(29,40,42,37)(30,44,45,38)(33,48,50,46)(34,51,43,36)(41,53,57,55)(49,52,56,54);(18,20,22,21)(19,23,24,25)(26,29,31,42)(27,33,35,50)(28,37,39,40)(30,41,45,57)(32,46,47,48)(34,49,43,56)(36,52,51,54)(38,53,44,55)

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, 4524);