Finite Group Databasebeta

← Prev (#26040691) Next (#26040693) →

AGL(1,𝔽₅)×C₁₉₃⋊C₃ #26040692

order	11580
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

direct product	AGL(1,𝔽₅)×C₁₉₃⋊C₃
unambiguous semidirect product	(AGL(1,𝔽₅)×C₁₉₃)⋊C₃

Splittings

Fitting, socle, derived, Hall	C₅×C₁₉₃ ⋊ C₃×C₄
Hall	AGL(1,𝔽₅)×C₁₉₃ ⋊ C₃
Hall	C₅×C₁₉₃⋊C₃ ⋊ C₄
Sylow	C₁₉₃ ⋊ C₃×AGL(1,𝔽₅)
Sylow	C₅ ⋊ C₄×C₁₉₃⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₉₃	C₃×C₄
prime radical	D₅×C₁₉₃⋊C₃	C₂
cosocle	D₅×C₁₉₃	C₂×C₃
LCS	G ▷ C₅×C₁₉₃
UCS	C₁

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

335 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×AGL(1,𝔽₅)×C₁₉₃⋊C₃, ΓL(1,𝔽₁₆)×C₁₉₃⋊C₃
maximal normal subgroup of	C₃×AGL(1,𝔽₅)×C₁₉₃⋊C₃
maximal quotient of	AGL(1,𝔽₅)×C₁₉₃⋊C₉, C₃×AGL(1,𝔽₅)×C₁₉₃⋊C₃, ΓL(1,𝔽₁₆)×C₁₉₃⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11580, 18);