C₅×D₁₄₄ #13083802

order	1440
isoclinism	isoclinic class of D₁₄₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅×D₁₄₄

Splittings

Fitting	C₅×C₉×C₁₆ ⋊ C₂
Hall	C₅×C₉ ⋊ D₁₆
Sylow	C₉ ⋊ C₅×D₁₆

Subgroups

	subgroup	G/H
center	C₂×C₅	D₇₂
commutator, cosocle	C₈×C₉	C₂²×C₅
Frattini	C₃×C₈	C₂×C₅×D₃
Fitting	C₅×C₉×C₁₆	C₂
socle	C₂×C₃×C₅	D₂₄
hypercenter	C₅×C₁₆	D₉
hypocenter	C₉	C₅×D₁₆
LCS	G ▷ C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×C₁₆

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 720

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21)(22,23,24,25,26,27,28,29,30);(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)(23,30)(24,29)(25,28)(26,27)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 119);

C5×D144 #13083802