C₁₇×#2351 #14525357

order	2176
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#2351

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₇
Frattini, cosocle	C₂³	C₂⁴×C₁₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

552 conjugacy classes of subgroups; only the 368 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 368 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) = 2176

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

Conjugacy classes & character table

850 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16927900, #16927905, #16930238, …
maximal subgroup of	C₁₇×#8766, C₁₇×#8767, C₁₇×#9176, …
maximal normal subgroup of	C₁₇×#8766, C₁₇×#8767, C₁₇×#9176, …
maximal quotient of	C₁₇×#13804, Q₈×C₁₇×#95, C₁₇×#13821, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1083);