C₁₇×#2187 #14525193

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

Aliases

direct product

C₁₇×#2187

Subgroups

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

256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 544

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)(24,27,33,36)(25,34,32,29)(28,37,35,31);(23,27)(24,31)(25,32)(28,29)(30,36)(33,37)(34,35);(19,21)

Conjugacy classes & character table

493 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16946424, #16946431, #16946458, …
maximal subgroup of	C₁₇×#12103, C₁₇×#12104, C₁₇×#12109, …
maximal normal subgroup of	C₁₇×#12103, C₁₇×#12104, C₁₇×#12109, …
maximal quotient of	C₁₇×#12105, C₁₇×#12161, C₁₇×#12281, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 919);