C₁₇×#12889 #16870633

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#12889

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

310 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 174 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) = 61
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 3 generators on 61 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21)(22,23)(24,27)(25,26)(28,29)(30,31)(32,44)(33,38)(34,52)(35,55)(36,56)(37,43)(39,48)(40,45)(41,54)(42,53)(46,58)(47,57)(49,61)(50,60)(51,59);(23,26)(27,29)(30,32,45,50,36,47,54,51,37,48,35,46,53,49,34,33)(31,38,52,61,42,58,55,39,43,59,41,57,56,60,40,44);(22,24,25,28)(23,27,26,29)(30,33,34,49,53,46,35,48,37,51,54,47,36,50,45,32)(31,39,40,58,56,61,41,38,43,44,55,60,42,57,52,59)

Conjugacy classes & character table

1292 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5877);