Finite Group Databasebeta

← Prev (#26044750) Next (#26044752) →

C₂²×C₄×C₇₃₉ #26044751

order	11824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 141696
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₄×C₇₃₉
multiplicative	(ℤ/23656)ˣ, (ℤ/35484)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₇₃₉
socle, prime radical	C₂³×C₇₃₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11824 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₇₃₉⋊#95, C₂²⋊(C₇₃₉⋊C₈), C₂×C₄×Dic₇₃₉, …
maximal subgroup of	#95×C₇₃₉, C₂²⋊C₈×C₇₃₉, C₂×C₄²×C₇₃₉, …
maximal normal subgroup of	#95×C₇₃₉, C₂²⋊C₈×C₇₃₉, C₂×C₄²×C₇₃₉, …
maximal quotient of	C₂×C₄²×C₇₃₉, C₂×C₂²⋊C₄×C₇₃₉, C₂×C₄⋊C₄×C₇₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11824, 10);