C₁₇×#1479 #14524485

order	2176
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#1479

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂×D₄
commutator	C₄	C₂²×C₈×C₁₇
Frattini, cosocle	C₄²	C₂³×C₁₇
socle	C₂²×C₁₇	C₂×C₂²⋊C₄
prime radical	C₂³×C₁₇	C₂²⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

248 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 124 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) = 41
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 41 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,22,21,23,24,25)(26,27)(28,35)(29,33)(30,39)(31,34)(32,37)(36,40)(38,41);(26,28,31,38)(27,32,34,40)(29,37,30,36)(33,41,39,35);(26,29,31,30)(27,33,34,39)(28,36,38,37)(32,35,40,41)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16925744, #16925749, #16925754, …
maximal subgroup of	C₁₇×#8323, C₁₇×#8324, C₁₇×#8325, …
maximal normal subgroup of	C₁₇×#8323, C₁₇×#8324, C₁₇×#8325, …
maximal quotient of	C₁₇×#7573, C₁₇×#7575, C₁₇×#7581, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 211);