Finite Group Databasebeta

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C₂×D₆₃₂₇ #38760926

order	25308
automorphism	Aut(G) order 49198752
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₂₆₅₄
direct product	C₂×D₆₃₂₇
unambiguous semidirect product	(C₂×C₉)⋊D₇₀₃
unambiguous semidirect product	(C₂×C₁₉)⋊D₃₃₃
unambiguous semidirect product	(C₂×C₃₇)⋊D₁₇₁

Splittings

Fitting	C₂×C₉×C₁₉×C₃₇ ⋊ C₂
derived, Hall	C₉×C₁₉×C₃₇ ⋊ C₂²
Hall	C₁₉×C₃₇ ⋊ C₂×D₉
Hall	C₉×C₃₇ ⋊ C₂×D₁₉
Hall	C₉×C₁₉ ⋊ C₂×D₃₇
Sylow	C₃₇ ⋊ C₂×D₁₇₁
Sylow	C₁₉ ⋊ C₂×D₃₃₃
Sylow	C₉ ⋊ C₂×D₇₀₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₆₃₂₇
commutator, hypocenter	C₉×C₁₉×C₃₇	C₂²
Frattini	C₃	C₂×D₂₁₀₉
Fitting	C₂×C₉×C₁₉×C₃₇	C₂
socle	C₂×C₃×C₁₉×C₃₇	D₃
LCS	G ▷ C₉×C₁₉×C₃₇
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6330 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₅₃₀₈
maximal normal subgroup of	D₂₅₃₀₈
maximal quotient of	Dic₁₂₆₅₄, D₂₅₃₀₈

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25308, 70);