C₁₇×#1788 #14524794

order	2176
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#1788

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₂²×#41×C₁₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

612 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 152 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)(22,23,24,25)(27,31)(28,29)(32,33);(26,27)(28,31)(29,33)(30,32);(19,21)(26,28,30,29)(27,31,32,33)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16926516, #16926530, #16931371, …
maximal subgroup of	C₁₇×#8465, C₁₇×#8467, C₁₇×#9345, …
maximal normal subgroup of	C₁₇×#8465, C₁₇×#8467, C₁₇×#9345, …
maximal quotient of	C₁₇×#8312, C₁₇×#8315, C₁₇×#8330, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 520);