Finite Group Databasebeta

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Dic₁₅×C₁₉₃ #26040682

order	11580
isoclinism	isoclinic class of D₁₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₁₅×C₁₉₃
unambiguous semidirect product	C₃⋊(Dic₅×C₁₉₃)

Splittings

derived, Hall	C₃×C₅ ⋊ C₄×C₁₉₃
Hall	C₃×C₅×C₁₉₃ ⋊ C₄
Hall	C₅×C₁₉₃ ⋊ Dic₃
Hall	C₃×C₁₉₃ ⋊ Dic₅
Sylow	C₅ ⋊ Dic₃×C₁₉₃
Sylow	C₃ ⋊ Dic₅×C₁₉₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉₃	D₁₅
commutator, hypocenter	C₃×C₅	C₄×C₁₉₃
Frattini	C₂	D₁₅×C₁₉₃
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₉₃	C₂
cosocle	C₂×C₃×C₅	C₂×C₁₉₃
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₁₉₃

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3474 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₄₅×C₁₉₃, Dic₁₅×C₁₉₃⋊C₃, C₃⋊Dic₁₅×C₁₉₃, …
maximal normal subgroup of	Dic₁₅×C₁₉₃⋊C₃, C₃×Dic₁₅×C₁₉₃
maximal quotient of	Dic₄₅×C₁₉₃, C₃⋊Dic₁₅×C₁₉₃, C₃×Dic₁₅×C₁₉₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11580, 8);