C₁₇×#2341 #14525347

order	2176
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₇×#2341

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₇
Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₂²×#41×C₁₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

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

normal subgroups only

This group has 872 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) = 1088

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

Conjugacy classes & character table

850 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16931506, #16931534, #17001954, …
maximal subgroup of	C₁₇×#9364, C₁₇×#9368, C₁₇×#17606, …
maximal normal subgroup of	C₁₇×#9364, C₁₇×#9368, C₁₇×#17606, …
maximal quotient of	C₁₇×#13801, Q₈×C₁₇×#95, C₁₇×#13820, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1073);