Finite Group Databasebeta

← Prev (#20294262) Next (#20294264) →

C₄×C₁₉₃⋊C₉ #20294263

order	6948
automorphism	?
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄×C₁₉₃⋊C₉
unambiguous semidirect product	(C₄×C₁₉₃)⋊C₉

Splittings

derived, Sylow	C₁₉₃ ⋊ C₄×C₉
Hall	C₄×C₁₉₃ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄	C₁₉₃⋊C₃
commutator, hypocenter	C₁₉₃	C₄×C₉
Frattini	C₂×C₃	C₂×C₁₉₃⋊C₃
Fitting	C₃×C₄×C₁₉₃	C₃
socle	C₂×C₃×C₁₉₃	C₂×C₃
LCS	G ▷ C₁₉₃
UCS	C₁ ◁ C₃×C₄

18 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

804 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×C₅×C₁₉₃⋊C₉, Dic₅×C₁₉₃⋊C₉, AGL(1,𝔽₅)×C₁₉₃⋊C₉
maximal normal subgroup of	C₄×C₅×C₁₉₃⋊C₉
maximal quotient of	C₄×C₅×C₁₉₃⋊C₉, Dic₅×C₁₉₃⋊C₉, AGL(1,𝔽₅)×C₁₉₃⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6948, 3);