C₁₇×#3138 #14526144

order	2176
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₇×#3138

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₇
prime radical	C₂×C₁₇×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

484 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 192 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 — 4 generators on 33 points:

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16931857, #16931862, #16931939, …
maximal subgroup of	C₁₇×#9424, C₁₇×#9425, C₁₇×#9438, …
maximal normal subgroup of	C₁₇×#9424, C₁₇×#9425, C₁₇×#9438, …
maximal quotient of	C₁₇×#20764, C₁₇×#21095, C₁₇×#21203, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1870);