C₁₇×#12044 #16869788

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#12044

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂×D₈
commutator	C₈	C₂²×C₈×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
socle, prime radical	C₂²×C₁₇	C₄×D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₈²×C₁₇ ◁ G

222 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 4352

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

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5032);