C₁₇×#1550 #14524556

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

Aliases

direct product

C₁₇×#1550

Subgroups

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

216 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 108 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)(19,23)(20,21)(24,25)(26,27,30,33,31,28,29,32);(18,19,22,24)(20,23,21,25)(26,28,31,27)(29,32,30,33);(18,20,22,21)(19,23,24,25)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16925880, #16925885, #16925892, …
maximal subgroup of	C₁₇×#8355, C₁₇×#8356, C₁₇×#8357, …
maximal normal subgroup of	C₁₇×#8355, C₁₇×#8356, C₁₇×#8357, …
maximal quotient of	C₁₇×#7577, C₁₇×#7589, C₁₇×#7615, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 282);