C₁₇×#11892 #16869636

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11855
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#11892

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₂⁴×C₁₇	SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ C₂³×C₈×C₁₇ ◁ G

396 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 122 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)(26,27,31,37,33,39,32,38)(28,40,43,50,45,55,44,54)(29,46,30,49,48,36,47,35)(34,41,51,42,53,57,52,56);(18,20)(19,22)(21,25)(23,24)(26,28,33,45)(27,34,39,53)(29,42,48,56)(30,41,47,57)(31,44,32,43)(35,40,49,55)(36,50,46,54)(37,52,38,51);(20,25)(22,24)(26,29,32,47,33,48,31,30)(27,35,37,46,39,49,38,36)(28,41,44,56,45,57,43,42)(34,50,51,55,53,54,52,40)

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, 4880);