C₁₇×#1996 #14525002

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#1996

Subgroups

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

324 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 116 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)(20,24)(21,22)(23,25)(26,27)(28,30,32,33)(29,31);(19,22)(23,24)(26,28)(27,30,31,33)(29,32);(18,20,21,25)(19,23,22,24)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16926525, #16926532, #16926600, …
maximal subgroup of	C₁₇×#8467, C₁₇×#8468, C₁₇×#8480, …
maximal normal subgroup of	C₁₇×#8467, C₁₇×#8468, C₁₇×#8480, …
maximal quotient of	C₁₇×#9878, C₁₇×#9879, C₁₇×#9880, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 728);