C₁₇×#12593 #16870337

order	4352
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₁₇ · Schur multiplier (H₂) = C₄²

Aliases

direct product

C₁₇×#12593

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₇	C₄²
commutator	C₄	C₂×C₄×C₈×C₁₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
socle	C₂²×C₁₇	C₂×#97
prime radical	C₂³×C₁₇	C₂×M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₇ ◁ G

338 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 222 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)(20,23)(21,22)(24,25)(26,27,31,37,32,39,47,54,33,38,46,53,30,36,29,35)(28,40,43,56,44,34,41,50,45,52,48,49,42,51,57,55);(19,22)(23,25)(26,28)(27,34,38,51)(29,41)(30,42)(31,48)(32,44)(33,45)(35,49,54,56)(36,40,39,52)(37,55,53,50)(43,46)(47,57);(18,20,21,24)(19,23,22,25)(26,29,30,46,33,47,32,31)(27,35,36,53,38,54,39,37)(28,41,42,43,45,57,44,48)(34,49,40,50,51,56,52,55)

Conjugacy classes & character table

1496 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5581);