C₁₇×#2163 #14525169

order	2176
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#2163

Subgroups

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

152 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 104 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)(26,27,28,32,29,33,34,39,30,31,35,37,36,38,40,41);(19,22)(23,25);(18,20,21,24)(19,23,22,25)(27,31)(32,37)(33,38)(39,41)

Conjugacy classes & character table

952 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921167, #16921171, #16921174, …
maximal subgroup of	C₁₇×#7143, C₁₇×#7144, C₁₇×#7146, …
maximal normal subgroup of	C₁₇×#7143, C₁₇×#7144, C₁₇×#7146, …
maximal quotient of	C₁₇×#12591, C₁₇×#12599, C₁₇×#12653, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 895);