C₁₇×#3362 #14526368

order	2176
nilpotency class	3
isoclinism	isoclinic class of D₄×D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#3362

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₇
prime radical	C₁₇×#550	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄×Q₈×C₁₇ ◁ G

392 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 192 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) = 1088

A minimal faithful permutation representation — 4 generators on 33 points:

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

Conjugacy classes & character table

595 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#17023867, #17023897, #17024342, …
maximal subgroup of	C₁₇×#19768, C₁₇×#19770, C₁₇×#19800, …
maximal normal subgroup of	C₁₇×#19768, C₁₇×#19770, C₁₇×#19800, …
maximal quotient of	Q₈×C₁₇×#103, C₁₇×#22540, C₁₇×#22738, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 2094);