C₁₇×#2169 #14525175

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×#2169

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	C₂×D₄×C₁₇	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₇ ◁ G

162 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 37
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 37 points:

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

Conjugacy classes & character table

952 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921765, #16946032, #16946039, …
maximal subgroup of	C₁₇×#7380, C₁₇×#12038, C₁₇×#12039, …
maximal normal subgroup of	C₁₇×#7380, C₁₇×#12038, C₁₇×#12039, …
maximal quotient of	C₁₇×#12039, C₁₇×#12051, C₁₇×#12054, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 901);