C₁₇×#2162 #14525168

order	2176
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#2162

Subgroups

	subgroup	G/H
center	C₄×C₈×C₁₇	C₂²
commutator	C₂	C₂²×C₁₆×C₁₇
Frattini, cosocle	C₂×C₈	C₂³×C₁₇
socle	C₂²×C₁₇	C₂²×C₈
prime radical	C₂³×C₁₇	C₂×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₁₇ ◁ G

160 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 120 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)(20,23)(21,22)(24,25)(26,27,28,31,29,32,34,37,30,33,35,38,36,39,40,41);(19,22)(23,25);(18,20,21,24)(19,23,22,25)

Conjugacy classes & character table

1360 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#16921165, #16921169, #16921172, …
maximal subgroup of	C₁₇×#7142, C₁₇×#7144, C₁₇×#7145, …
maximal normal subgroup of	C₁₇×#7142, C₁₇×#7144, C₁₇×#7145, …
maximal quotient of	C₁₇×#12590, C₄×C₁₇×C₂²⋊C₁₆, C₄×C₁₇×C₄⋊C₁₆, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 894);