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C₁₃×C₁₇×D₂₁ #22604641

order	9282
isoclinism	isoclinic class of D₂₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₁₇×D₂₁
unambiguous semidirect product	C₃⋊(C₁₃×D₇×C₁₇)
unambiguous semidirect product	C₇⋊(D₃×C₁₃×C₁₇)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃×C₁₇	D₂₁
commutator, hypocenter	C₃×C₇	C₂×C₁₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₁₇	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₁₃×C₁₇

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2652 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₃×D₁₇×D₂₁, C₁₇×D₁₃×D₂₁, D₂₁×D₂₂₁, …
maximal normal subgroup of	C₁₃×D₁₇×D₂₁, C₁₇×D₁₃×D₂₁, D₂₁×D₂₂₁, …
maximal quotient of	C₁₃×C₁₇×Dic₂₁, C₂×C₁₃×C₁₇×D₂₁, C₁₃×C₁₇×D₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9282, 17);