C₁₇×#2007 #14525013

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

Aliases

direct product

C₁₇×#2007

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₁₇×#537	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

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

normal subgroups only

This group has 370 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)(22,23,27,31)(24,32,34,37)(25,30,26,29)(28,35,36,33);(18,19)(20,21)(22,24)(23,28)(25,35)(26,33)(27,34)(29,37)(30,32)(31,36);(19,21)(22,24)(23,28)(25,33)(26,35)(27,34)(29,32)(30,37)(31,36)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921852, #16946396, #16946410, …
maximal subgroup of	C₁₇×#7409, C₁₇×#12098, C₁₇×#12100, …
maximal normal subgroup of	C₁₇×#7409, C₁₇×#12098, C₁₇×#12100, …
maximal quotient of	C₁₇×#9934, C₁₇×#9935, C₁₇×#9936, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 739);