Finite Group Databasebeta

← Prev (#24925255) Next (#24925257) →

C₄×C₅₄₁⋊C₅ #24925256

order	10820
automorphism	?
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄×C₅₄₁⋊C₅
unambiguous semidirect product	(C₄×C₅₄₁)⋊C₅

Splittings

Fitting, Hall	C₄×C₅₄₁ ⋊ C₅
derived, Sylow	C₅₄₁ ⋊ C₄×C₅

Subgroups

	subgroup	G/H
center, hypercenter	C₄	C₅₄₁⋊C₅
commutator, hypocenter	C₅₄₁	C₄×C₅
Frattini	C₂	C₂×C₅₄₁⋊C₅
Fitting	C₄×C₅₄₁	C₅
socle, cosocle	C₂×C₅₄₁	C₂×C₅
prime radical	C₂×C₅₄₁⋊C₅	C₂
LCS	G ▷ C₅₄₁
UCS	C₁ ◁ C₄

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

452 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×C₄×C₅₄₁⋊C₅, C₄×(C₅₄₁⋊C₃)⋊C₅, Dic₃×C₅₄₁⋊C₅
maximal normal subgroup of	C₃×C₄×C₅₄₁⋊C₅, C₄×(C₅₄₁⋊C₃)⋊C₅
maximal quotient of	C₃×C₄×C₅₄₁⋊C₅, Dic₃×C₅₄₁⋊C₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10820, 3);