C₁₇×#2901 #14525907

order	2176
nilpotency class	3
isoclinism	isoclinic class of #576
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₇×#2901

Subgroups

	subgroup	G/H
center	C₄×C₁₇	C₂²×D₄
commutator	C₄	C₂³×C₄×C₁₇
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₇
socle	C₂×C₁₇	C₂²×C₂²⋊C₄
prime radical	C₁₇×#585	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂×#41×C₁₇ ◁ G

738 conjugacy classes of subgroups; only the 340 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 340 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 — 4 generators on 33 points:

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

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#17050280, #17050291, #17055189, …
maximal subgroup of	C₁₇×#22461, C₁₇×#22462, C₁₇×#22898, …
maximal normal subgroup of	C₁₇×#22461, C₁₇×#22462, C₁₇×#22898, …
maximal quotient of	C₁₇×#17438, C₁₇×#17439, C₁₇×#17453, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1633);