C₁₇×#3152 #14526158

order	2176
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₇×#3152

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₇
prime radical	C₁₇×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

552 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 224 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) = 1088

A minimal faithful permutation representation — 4 generators on 37 points:

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16931842, #16931884, #16931924, …
maximal subgroup of	C₁₇×#9421, C₁₇×#9429, C₁₇×#9435, …
maximal normal subgroup of	C₁₇×#9421, C₁₇×#9429, C₁₇×#9435, …
maximal quotient of	C₁₇×#19622, C₁₇×#19626, C₁₇×#19630, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1884);