C₁₇×#2004 #14525010

order	2176
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2004

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₁₇×#535	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

394 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 37
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23)(24,30)(25,33)(26,29)(27,31)(28,35)(32,37)(34,36);(22,24,26,32)(23,27,29,36)(25,34,35,31)(28,37,33,30);(19,21)(25,35)(27,36)(28,33)(31,34)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2004, #17061232, #17061248, …
maximal subgroup of	C₂×C₁₇×#2004, C₁₇×#23399, C₁₇×#23401, …
maximal normal subgroup of	C₂×C₁₇×#2004, C₁₇×#23399, C₁₇×#23401, …
maximal quotient of	C₁₇×#9916, C₁₇×#9918, C₁₇×#9924, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 736);