C₁₇×#1465 #14524471

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#1465

Subgroups

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

316 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 100 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)(20,24,25,22)(21,23)(26,27,29,31,30,32,28,33);(18,20)(19,22)(21,25)(23,24);(26,28,30,29)(27,31,32,33)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921436, #16921441, #16921634, …
maximal subgroup of	C₁₇×#7247, C₁₇×#7249, C₁₇×#7321, …
maximal normal subgroup of	C₁₇×#7247, C₁₇×#7249, C₁₇×#7321, …
maximal quotient of	C₁₇×#7616, C₁₇×#7617, C₁₇×#7620, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 197);