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C₁₃×#10620321 #22555434

order	8541
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

C₁₃×#10620321

Splittings

derived, Sylow	C₇₃ ⋊ C₉×C₁₃
Hall	C₁₃×C₇₃ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃	C₇₃⋊C₃
commutator, hypocenter	C₇₃	C₉×C₁₃
Frattini	C₃	C₁₃×C₇₃⋊C₃
Fitting, socle	C₃×C₁₃×C₇₃	C₃
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₃×C₁₃

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1053 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₃×#10620321, C₁₃×#10620321⋊C₂, D₁₃×#10620321, …
maximal normal subgroup of	C₂×C₁₃×#10620321, C₁₃×#10620321⋊C₂, D₁₃×#10620321, …
maximal quotient of	C₂×C₁₃×#10620321, C₁₃×C₂²⋊#10620321

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8541, 3);