C₁₇×#1599 #14524605

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#1599

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₂²×D₄×C₁₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

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

normal subgroups only

This group has 266 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) = 33
transitive degree	μ_t(G) = 544

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

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16947073, #16947083, #16947090, …
maximal subgroup of	C₁₇×#12208, C₁₇×#12210, C₁₇×#12211, …
maximal normal subgroup of	C₁₇×#12208, C₁₇×#12210, C₁₇×#12211, …
maximal quotient of	C₁₇×#7739, C₁₇×#7741, C₁₇×#7747, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 331);