Finite Group Databasebeta

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#10624500⋊C₂ #13090536

order	1458
isoclinism	isoclinic class of #10624500⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product

#10624500⋊C₂

Splittings

Fitting, Sylow	#10624500 ⋊ C₂
derived	C₈₁ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, hypocenter	C₈₁	C₂×C₉
Frattini	C₃×C₂₇	C₃×D₃
Fitting	#10624500	C₂
socle	C₃	#6864⋊C₂
prime radical	D₈₁⋊C₃	C₃
cosocle	C₈₁⋊C₃	C₂×C₃
LCS	G ▷ C₈₁
UCS	C₁

39 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 81
transitive degree	μ_t(G) = 81

Polycyclic presentation:

2,3^6|b^3=d,c^3=e,d^3=f,f^3=g,b^a=b^2d^2f^2g^2,d^a=d^2f^2g^2,f^a=f^2g^2,g^a=g^2,c^b=cf,e^b=eg,d^c=dg^2

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72221799, C₂×#10624500⋊C₂
maximal normal subgroup of	#72221799, C₂×#10624500⋊C₂
maximal quotient of	C₂×#10624500⋊C₂, #72277437

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 610);