C₁₇×#1505 #14524511

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#1505

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₁₇×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 272 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) = 33
transitive degree	μ_t(G) = 544

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)(20,24)(21,23)(22,25)(27,30,31,32);(19,23)(20,21)(24,25)(26,27)(28,32)(29,31)(30,33);(18,20,22,21)(19,24,25,23)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16926177, #16926191, #16926676, …
maximal subgroup of	C₁₇×#8412, C₁₇×#8414, C₁₇×#8491, …
maximal normal subgroup of	C₁₇×#8412, C₁₇×#8414, C₁₇×#8491, …
maximal quotient of	C₁₇×#7580, C₁₇×#7587, C₁₇×#7591, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 237);