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C₇×C₉×D₅×C₂₃ #28408015

order	14490
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₉×D₅×C₂₃
unambiguous semidirect product	C₅⋊(C₂×C₇×C₉×C₂₃)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₉×C₂₃	D₅
commutator, hypocenter	C₅	C₂×C₇×C₉×C₂₃
Frattini	C₃	C₃×C₇×D₅×C₂₃
Fitting	C₅×C₇×C₉×C₂₃	C₂
socle	C₃×C₅×C₇×C₂₃	C₂×C₃
prime radical	C₃×C₇×D₅×C₂₃	C₃
cosocle	C₃×C₅	C₂×C₃×C₇×C₂₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₇×C₉×C₂₃

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7245

Conjugacy classes & character table

5796 conjugacy classes. The character table is too large to display.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14490, 6);