Finite Group Databasebeta

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C₁₇×C₃⋊D₃×C₂₃ #20296392

order	7038
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇×C₂₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₁₇×C₃⋊D₃×C₂₃
unambiguous semidirect product	C₃⋊(D₃×C₁₇×C₂₃)

Splittings

Fitting, socle, Hall	C₃²×C₁₇×C₂₃ ⋊ C₂
derived, Sylow	C₃² ⋊ C₂×C₁₇×C₂₃
Hall	C₃²×C₂₃ ⋊ C₂×C₁₇
Hall	C₃²×C₁₇ ⋊ C₂×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇×C₂₃	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₁₇×C₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇×C₂₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₇×C₂₃

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2346 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₇×C₃⋊D₃×D₂₃, C₃⋊D₃×C₂₃×D₁₇, C₃⋊D₃×D₃₉₁, …
maximal normal subgroup of	C₁₇×C₃⋊D₃×D₂₃, C₃⋊D₃×C₂₃×D₁₇, C₃⋊D₃×D₃₉₁, …
maximal quotient of	C₁₇×C₂₃×C₃⋊Dic₃, C₂×C₁₇×C₃⋊D₃×C₂₃, C₅×C₁₇×C₃⋊D₃×C₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7038, 17);