C₁₇×#1619 #14524625

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#1619

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

336 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 76 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)(18,19)(20,22)(21,24)(23,25)(26,27)(28,31)(29,32)(30,33);(19,22)(20,25)(23,24)(27,31)(28,29)(32,33);(27,32)(28,29)(31,33)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16922140, #16955034, D₁₇×#1619, …
maximal subgroup of	C₁₇×#7515, C₁₇×#13673, C₂×C₁₇×#1619, …
maximal normal subgroup of	C₁₇×#7515, C₁₇×#13673, C₂×C₁₇×#1619, …
maximal quotient of	C₁₇×#7734, C₁₇×#7737, C₁₇×#7738, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 351);