C₁₇×#11960 #16869704

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11858
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#11960

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₁₇×#3147	C₂
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

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

normal subgroups only

This group has 392 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) = 57
transitive degree	μ_t(G) = 2176

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

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4948);