Finite Group Databasebeta

← Prev (#91080) Next (#91082) →

C₁₆×D₁₅ #91081

order	480
isoclinism	isoclinic class of D₁₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

C₁₆×D₁₅

Splittings

Fitting	C₃×C₅×C₁₆ ⋊ C₂
derived, Hall	C₃×C₅ ⋊ C₂×C₁₆
Sylow	C₅ ⋊ D₃×C₁₆
Sylow	C₃ ⋊ D₅×C₁₆

Subgroups

	subgroup	G/H
center, hypercenter	C₁₆	D₁₅
commutator, hypocenter	C₃×C₅	C₂×C₁₆
Frattini	C₈	C₂×D₁₅
Fitting	C₃×C₅×C₁₆	C₂
socle	C₂×C₃×C₅	C₂×C₈
prime radical	C₂×D₁₅	C₈
cosocle	C₃×C₅×C₈	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₁₆

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 2 generators on 24 points:

(2,3)(4,5)(7,8);(1,2,4,5,3)(6,7,8)(9,10,11,14,12,15,17,20,13,16,18,21,19,22,23,24)

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11745814, #11745817, D₁₅×C₃₂, …
maximal normal subgroup of	#11745814, #11745817, D₁₅×C₃₂, …
maximal quotient of	D₁₅×C₃₂, #11746268, C₁₆×Dic₁₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 157);