C₁₇×#1828 #14524834

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1828
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#1828

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#381
commutator	C₂³	C₂²×C₄×C₁₇
Frattini, cosocle	C₂⁴	C₂³×C₁₇
prime radical	C₂²×D₄×C₁₇	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂⁴×C₁₇ ◁ G

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

normal subgroups only

This group has 296 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) = 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)(20,26,28,23)(21,29)(22,25)(24,30)(27,31,33,32);(18,20)(19,23)(21,27)(22,28)(24,31)(25,26)(29,32)(30,33);(18,21)(19,24,25,29)(20,27)(22,30)(23,31,26,32)(28,33)

Conjugacy classes & character table

493 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16949939, #16949944, #16949949, …
maximal subgroup of	C₁₇×#12725, C₁₇×#12726, C₁₇×#12727, …
maximal normal subgroup of	C₁₇×#12725, C₁₇×#12726, C₁₇×#12727, …
maximal quotient of	C₁₇×#8734, C₁₇×#8735, C₁₇×#8736, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 560);