Finite Group Databasebeta

← Prev (#26042332) Next (#26042334) →

C₂×D₁₈₁⋊C₁₆ #26042333

order	11584
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂×D₁₈₁⋊C₁₆
unambiguous semidirect product	D₁₈₁⋊(C₂×C₁₆)

Splittings

C₁₈₁ ⋊ C₂²×C₁₆

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₈	#10624382
commutator, hypocenter	C₁₈₁	C₂²×C₁₆
Frattini	C₄	C₂²×#10624382
Fitting	C₂×C₈×C₁₈₁	C₄
socle	C₂²×C₁₈₁	C₂×C₈
prime radical	C₂²×D₁₈₁	C₈
cosocle	#13089678	C₂³
LCS	G ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₈

98 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

784 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	(C₂×#10624382)⋊C₁₆, #37548777, #37548778, …
maximal normal subgroup of	(C₂×#10624382)⋊C₁₆, #37548777, #37548778, …
maximal quotient of	C₄×D₁₈₁⋊C₁₆, C₂×#26042165, D₁₈₁⋊(C₂²⋊C₁₆), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 1603);