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C₁₃×C₁₉₃⋊C₃ #21419087

order	7527
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₁₉₃⋊C₃
unambiguous semidirect product	C₁₉₃⋊(C₃×C₁₃)

Splittings

Fitting, socle, Hall	C₁₃×C₁₉₃ ⋊ C₃
derived, Sylow	C₁₉₃ ⋊ C₃×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	C₁₉₃⋊C₃
commutator, hypocenter	C₁₉₃	C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₉₃	C₃
LCS	G ▷ C₁₉₃
UCS	C₁ ◁ C₁₃

8 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

871 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₃×C₁₉₃⋊C₃, C₁₃×D₁₉₃⋊C₃, D₁₃×C₁₉₃⋊C₃, …
maximal normal subgroup of	C₂×C₁₃×C₁₉₃⋊C₃, C₁₃×D₁₉₃⋊C₃, D₁₃×C₁₉₃⋊C₃, …
maximal quotient of	C₂×C₁₃×C₁₉₃⋊C₃, C₁₃×C₁₉₃⋊C₉, C₃×C₁₃×C₁₉₃⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7527, 2);