C₁₇×#2186 #14525192

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2186

Subgroups

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

230 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 68 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)(23,28)(24,27)(25,32)(29,37)(30,36)(31,34)(33,35);(22,23)(24,29)(25,33)(26,30)(27,35)(28,32)(31,36)(34,37);(19,21)(22,24,26,27)(23,29,30,35)(25,31,34,32)(28,33,36,37)

Conjugacy classes & character table

493 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2186, #17188099, #17188122, …
maximal subgroup of	C₂×C₁₇×#2186, C₁₇×#33516, C₁₇×#33519, …
maximal normal subgroup of	C₂×C₁₇×#2186, C₁₇×#33516, C₁₇×#33519, …
maximal quotient of	C₁₇×#12104, C₁₇×#12160, C₁₇×#12280, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 918);