Finite Group Databasebeta

← Prev (#14523387) Next (#14523389) →

C₉×D₅×C₂₃ #14523388

order	2070
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₅×C₂₃
unambiguous semidirect product	C₅⋊(C₂×C₉×C₂₃)

Splittings

Fitting, Hall	C₅×C₉×C₂₃ ⋊ C₂
derived, Sylow	C₅ ⋊ C₂×C₉×C₂₃
Hall	C₅×C₂₃ ⋊ C₂×C₉
Hall	C₅×C₉ ⋊ C₂×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₂₃	D₅
commutator, hypocenter	C₅	C₂×C₉×C₂₃
Frattini	C₃	C₃×D₅×C₂₃
Fitting	C₅×C₉×C₂₃	C₂
socle	C₃×C₅×C₂₃	C₂×C₃
prime radical	C₃×D₅×C₂₃	C₃
cosocle	C₃×C₅	C₂×C₃×C₂₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₉×C₂₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1035

A minimal faithful permutation representation — 2 generators on 37 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(11,14)(12,13)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₉×AGL(1,𝔽₅)×C₂₃, C₉×C₂₃⋊AGL(1,𝔽₅), C₂₃×C₉⋊AGL(1,𝔽₅), …
maximal normal subgroup of	C₉×AGL(1,𝔽₅)×C₂₃, C₉×C₂₃⋊AGL(1,𝔽₅), C₂₃×C₉⋊AGL(1,𝔽₅), …
maximal quotient of	C₉×Dic₅×C₂₃, C₂×C₉×D₅×C₂₃, C₇×C₉×D₅×C₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2070, 3);