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C₂×D₇×C₁₉₇ #19149448

order	5516
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₇×C₁₉₇
unambiguous semidirect product	C₇⋊(C₂²×C₁₉₇)
unambiguous semidirect product	(C₂×C₇)⋊(C₂×C₁₉₇)

Splittings

Fitting, socle	C₂×C₇×C₁₉₇ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂²×C₁₉₇
Hall	C₇×C₁₉₇ ⋊ C₂²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉₇	D₇
commutator, hypocenter	C₇	C₂²×C₁₉₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₉₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₁₉₇

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1970 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×AGL(1,𝔽₇)×C₁₉₇, D₃×D₇×C₁₉₇, C₂×D₂₁×C₁₉₇, …
maximal normal subgroup of	C₂×AGL(1,𝔽₇)×C₁₉₇, C₂×C₃×D₇×C₁₉₇, C₂×C₅×D₇×C₁₉₇, …
maximal quotient of	D₃×D₇×C₁₉₇, C₂×D₂₁×C₁₉₇, C₂×C₃×D₇×C₁₉₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5516, 15);