C₁₇×#1819 #14524825

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#1819

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₁₇
Frattini, cosocle	C₂⁴	C₂³×C₁₇
prime radical	C₂⁵×C₁₇	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂⁵×C₁₇ ◁ G

504 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 112 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 — 3 generators on 33 points:

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921348, #16921697, #16926900, …
maximal subgroup of	C₁₇×#7213, C₁₇×#7349, C₁₇×#8535, …
maximal normal subgroup of	C₁₇×#7213, C₁₇×#7349, C₁₇×#8535, …
maximal quotient of	C₁₇×#8698, C₁₇×#8700, C₁₇×#8702, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 551);