C₁₇×#2011 #14525017

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#2011

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 510 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) = 1088

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)(20,21)(26,27)(28,31)(29,32)(30,33);(19,21)(22,23)(24,25)(27,31)(28,29)(32,33);(23,25)(27,32)(28,29)(31,33)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921831, #16923021, #16923025, …
maximal subgroup of	C₁₇×#7402, C₁₇×#7734, C₁₇×#7735, …
maximal normal subgroup of	C₁₇×#7402, C₁₇×#7734, C₁₇×#7735, …
maximal quotient of	C₁₇×#9946, C₁₇×#9952, C₁₇×#9962, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 743);