C₁₇×#11896 #16869640

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11858
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#11896

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

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

normal subgroups only

This group has 390 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) = 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)(26,27,30,36,32,38,31,37)(28,39,41,55,43,49,42,53)(29,44,46,35,48,54,47,34)(33,45,50,40,52,56,51,57);(18,20)(19,22)(21,25)(23,24)(26,28,32,43)(27,33,38,52)(29,45,48,56)(30,42,31,41)(34,53,35,55)(36,51,37,50)(39,44,49,54)(40,46,57,47);(20,25)(22,24)(26,29,30,46,32,48,31,47)(27,34,37,54,38,35,36,44)(28,40,41,56,43,57,42,45)(33,49,51,55,52,39,50,53)

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, 4884);