C₁₇×#2127 #14525133

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2127
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2127

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	C₂×#99
commutator	C₂×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×D₄	C₂³×C₁₇
prime radical	C₁₇×#535	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂³×C₁₇ ◁ C₂²×D₄×C₁₇ ◁ G

286 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 33
transitive degree	μ_t(G) = 272

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16949856, #16949859, #16949950, …
maximal subgroup of	C₁₇×#12707, C₁₇×#12708, C₁₇×#12727, …
maximal normal subgroup of	C₁₇×#12707, C₁₇×#12708, C₁₇×#12727, …
maximal quotient of	C₁₇×#11432, C₁₇×#11448, C₁₇×#11479, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 859);