Finite Group Databasebeta

← Prev (#23749133) Next (#23749135) →

C₄×C₂²⋊C₄×C₁₄₉ #23749134

order	9536
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₄₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product	C₄×C₂²⋊C₄×C₁₄₉
unambiguous semidirect product	C₂²⋊(C₄²×C₁₄₉)

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₄₉	C₂²
commutator	C₂	C₂×C₄²×C₁₄₉
Frattini, cosocle	C₂³	C₂³×C₁₄₉
socle	C₂³×C₁₄₉	C₂³
prime radical	C₂⁴×C₁₄₉	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₄₉ ◁ G

258 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5960 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#34042539, #34042544, #34042577, …
maximal subgroup of	#1282×C₁₄₉, #1284×C₁₄₉, #1297×C₁₄₉, …
maximal normal subgroup of	#1282×C₁₄₉, #1284×C₁₄₉, #1297×C₁₄₉, …
maximal quotient of	C₄×#95×C₁₄₉, C₂²⋊#95×C₁₄₉, #1434×C₁₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 58);