C₁₇×#3392 #14526398

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×#3392

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

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

normal subgroups only

This group has 404 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)(19,23)(24,25)(26,27,29,32)(28,30,33,31);(18,19,22,23)(20,24,21,25);(18,20,22,21)(19,24,23,25)(27,30)(28,33)(31,32);(18,21,22,20)(19,24,23,25)

Conjugacy classes & character table

595 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#17023852, #17023892, #17024327, …
maximal subgroup of	C₁₇×#19767, C₁₇×#19770, C₁₇×#19799, …
maximal normal subgroup of	C₁₇×#19767, C₁₇×#19770, C₁₇×#19799, …
maximal quotient of	C₁₇×#22540, C₁₇×#22542, Q₈×C₁₇×#106, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 2124);