C₁₇×#2276 #14525282

order	2176
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₁₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₇×#2276

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	C₂⁴
commutator	C₂	C₂²×C₄²×C₁₇
Frattini, cosocle	C₂³	C₂⁴×C₁₇
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

628 conjugacy classes of subgroups.

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

Conjugacy classes & character table

1156 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#16931226, #16931240, #17001539, …
maximal subgroup of	C₁₇×#9324, C₁₇×#9326, C₁₇×#17549, …
maximal normal subgroup of	C₁₇×#9324, C₁₇×#9326, C₁₇×#17549, …
maximal quotient of	C₁₇×#13750, C₁₇×#13783, C₁₇×#13786, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1008);

C17×#2276 #14525282