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#520×C₂₃₉ #29504424

order	15296
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃₉ · Schur multiplier (H₂) = C₂⁵

Aliases

#520×C₂₃₉

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃₉	C₂⁴
commutator	C₂	C₂³×C₄×C₂₃₉
Frattini, cosocle	C₂²	C₂⁴×C₂₃₉
prime radical	C₂×#41×C₂₃₉	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃₉ ◁ G

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7648

Conjugacy classes & character table

8126 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#44484774, #44484781, #44484917, …
maximal subgroup of	#1859×C₂₃₉, #1860×C₂₃₉, #1882×C₂₃₉, …
maximal normal subgroup of	#1859×C₂₃₉, #1860×C₂₃₉, #1882×C₂₃₉, …
maximal quotient of	#2274×C₂₃₉, #2275×C₂₃₉, #2276×C₂₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15296, 201);