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C₄×D₆₃ #92609

order	504
isoclinism	isoclinic class of D₆₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

C₄×D₆₃

Splittings

Fitting	C₄×C₇×C₉ ⋊ C₂
derived, Hall	C₇×C₉ ⋊ C₂×C₄
Sylow	C₉ ⋊ C₄×D₇
Sylow	C₇ ⋊ C₄×D₉

Subgroups

	subgroup	G/H
center, hypercenter	C₄	D₆₃
commutator, hypocenter	C₇×C₉	C₂×C₄
Frattini	C₂×C₃	C₂×D₂₁
Fitting	C₄×C₇×C₉	C₂
socle	C₂×C₃×C₇	C₂×D₃
prime radical	C₂×D₆₃	C₂
cosocle	C₂×C₇×C₉	C₂²
LCS	G ▷ C₇×C₉
UCS	C₁ ◁ C₄

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 252

A minimal faithful permutation representation — 2 generators on 20 points:

(2,3)(4,5)(6,7)(9,11)(10,14)(12,13)(15,16);(1,2,4,6,7,5,3)(8,16,11,14,13,12,10,9,15)(17,18,19,20)

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₆₃⋊C₈, #11758855, C₈×D₆₃, …
maximal normal subgroup of	D₆₃⋊C₈, #11758855, C₈×D₆₃, …
maximal quotient of	C₈×D₆₃, #11758921, C₄×Dic₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 35);