C₁₇×#3573 #14526579

order	2176
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₁₇×#3573

Subgroups

	subgroup	G/H
center	C₈×C₁₇	C₂⁴
commutator	C₂	C₂⁴×C₄×C₁₇
Frattini, cosocle	C₄	C₂⁵×C₁₇
socle	C₂×C₁₇	C₂⁴×C₄
prime radical	C₁₇×#585	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₇ ◁ G

1424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 5 generators on 49 points:

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

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	#16949772, #16949776, #17040286, …
maximal subgroup of	C₁₇×#12684, C₁₇×#12685, C₁₇×#21477, …
maximal normal subgroup of	C₁₇×#12684, C₁₇×#12685, C₁₇×#21477, …
maximal quotient of	C₁₇×#60058, C₁₇×#60065, C₁₇×#60100, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 2305);

C17×#3573 #14526579