Finite Group Databasebeta

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C₂×D₉×C₁₉₇ #20296807

order	7092
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₉×C₁₉₇
unambiguous semidirect product	C₉⋊(C₂²×C₁₉₇)
unambiguous semidirect product	(C₂×C₉)⋊(C₂×C₁₉₇)

Splittings

Fitting	C₂×C₉×C₁₉₇ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂²×C₁₉₇
Hall	C₉×C₁₉₇ ⋊ C₂²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉₇	D₉
commutator, hypocenter	C₉	C₂²×C₁₉₇
Frattini	C₃	C₂×D₃×C₁₉₇
Fitting	C₂×C₉×C₁₉₇	C₂
socle	C₂×C₃×C₁₉₇	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₁₉₇

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2364 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₅×D₉×C₁₉₇, C₂×D₄₅×C₁₉₇, C₂×C₅×D₉×C₁₉₇
maximal normal subgroup of	C₂×C₅×D₉×C₁₉₇
maximal quotient of	D₅×D₉×C₁₉₇, C₂×D₄₅×C₁₉₇, C₂×C₅×D₉×C₁₉₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7092, 11);