C₁₇×#3407 #14526413

order	2176
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#3407

Subgroups

	subgroup	G/H
center	C₈×C₁₇	C₂⁴
commutator	C₂	C₂³×C₈×C₁₇
Frattini, cosocle	C₈	C₂⁴×C₁₇
socle	C₂×C₁₇	C₂³×C₈
prime radical	C₂×#41×C₁₇	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₇ ◁ G

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 4 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,26,22,27,31,39,23,25,32,37,33,38,43,47)(20,24,29,35,30,36,42,46,28,34,40,44,41,45,48,49);(18,20)(19,24)(21,29)(22,30)(23,28)(25,34)(26,35)(27,36)(31,42)(32,40)(33,41)(37,44)(38,45)(39,46)(43,48)(47,49);(20,28)(24,34)(29,40)(30,41)(35,44)(36,45)(42,48)(46,49);(19,25)(24,34)(26,37)(27,38)(35,44)(36,45)(39,47)(46,49)

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	#16949449, #16950485, #16950799, …
maximal subgroup of	C₁₇×#12618, C₁₇×#12833, C₁₇×#12915, …
maximal normal subgroup of	C₁₇×#12618, C₁₇×#12833, C₁₇×#12915, …
maximal quotient of	C₁₇×#33324, C₁₇×#33326, C₁₇×#33333, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 2139);

C17×#3407 #14526413