C₉×D₂₅ #90637

order	450
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₂₅
unambiguous semidirect product	C₂₅⋊(C₂×C₉)

Splittings

Fitting, Hall	C₉×C₂₅ ⋊ C₂
derived, Sylow	C₂₅ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₂₅
commutator, hypocenter	C₂₅	C₂×C₉
Frattini, socle	C₃×C₅	C₃×D₅
Fitting	C₉×C₂₅	C₂
prime radical	C₃×D₂₅	C₃
cosocle	C₃×C₂₅	C₂×C₃
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₉

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 225

A minimal faithful permutation representation — 2 generators on 34 points:

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

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₉×#1035, C₉⋊#1035, D₉×D₂₅, …
maximal normal subgroup of	C₉×#1035, C₉⋊#1035, D₉×D₂₅, …
maximal quotient of	C₉×Dic₂₅, C₂×C₉×D₂₅, C₂₇×D₂₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(450, 2);

C9×D25 #90637

Aliases

Splittings

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₉×D₂₅ #90637