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Dic₇×C₁₉₃ #19129236

order	5404
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₇×C₁₉₃
unambiguous semidirect product	C₇⋊(C₄×C₁₉₃)

Splittings

derived, Sylow	C₇ ⋊ C₄×C₁₉₃
Hall	C₇×C₁₉₃ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉₃	D₇
commutator, hypocenter	C₇	C₄×C₁₉₃
Frattini	C₂	D₇×C₁₉₃
Fitting, socle	C₂×C₇×C₁₉₃	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₁₉₃

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1930 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×Dic₇×C₁₉₃, Dic₂₁×C₁₉₃, Dic₇×C₁₉₃⋊C₃, …
maximal normal subgroup of	C₃×Dic₇×C₁₉₃, Dic₇×C₁₉₃⋊C₃, ΓL(1,𝔽₈)⋊C₄×C₁₉₃, …
maximal quotient of	C₃×Dic₇×C₁₉₃, Dic₂₁×C₁₉₃, C₅×Dic₇×C₁₉₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5404, 2);