Finite Group Databasebeta

← Prev (#26039434) Next (#26039436) →

C₇×#13109900 #26039435

order	11466
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₇×#13109900

Splittings

derived	C₇×C₁₃ ⋊ C₂×C₇×C₉
Hall	C₇×#11717941 ⋊ C₂
Hall	C₇×C₁₃×D₇ ⋊ C₉
Hall	C₇²×C₁₃ ⋊ C₂×C₉
Hall	C₇×D₇ ⋊ C₁₃⋊C₉
Sylow	C₇² ⋊ C₂×C₁₃⋊C₉
Sylow	C₁₃ ⋊ C₇×D₇⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇	#10587720
commutator, hypocenter	C₇×C₁₃	C₂×C₇×C₉
Frattini	C₃	C₇×#10587720
Fitting, socle	C₃×C₇²×C₁₃	C₂×C₃
prime radical	C₃×C₇×C₁₃×D₇	C₃
cosocle	C₃×C₇×C₁₃	C₂×C₃×C₇
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₃×C₇

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

567 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₇×#13109896⋊C₂, #13109900⋊D₇, D₇×#13109900, …
maximal normal subgroup of	C₇×#13109896⋊C₂, #13109900⋊D₇, D₇×#13109900, …
maximal quotient of	C₇×#15692569, C₂×C₇×#13109900

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 78);