Finite Group Databasebeta

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C₂×C₉×D₁₉₇ #20296808

order	7092
isoclinism	isoclinic class of D₁₉₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₉×D₁₉₇
unambiguous semidirect product	C₁₉₇⋊(C₂²×C₉)
unambiguous semidirect product	(C₂×C₁₉₇)⋊(C₂×C₉)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	D₁₉₇
commutator, hypocenter	C₁₉₇	C₂²×C₉
Frattini	C₃	C₂×C₃×D₁₉₇
Fitting	C₂×C₉×C₁₉₇	C₂
socle	C₂×C₃×C₁₉₇	C₂×C₃
LCS	G ▷ C₁₉₇
UCS	C₁ ◁ C₂×C₉

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₅×D₁₉₇, C₂×C₉×D₉₈₅, C₂×C₅×C₉×D₁₉₇
maximal normal subgroup of	C₂×C₅×C₉×D₁₉₇
maximal quotient of	C₉×D₅×D₁₉₇, C₂×C₉×D₉₈₅, C₂×C₅×C₉×D₁₉₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7092, 12);