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C₅×#4294⋊D₇ #26046100

order	11970
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×#4294⋊D₇
unambiguous semidirect product	#4294⋊(C₅×D₇)

Splittings

derived, Hall	C₇×C₁₉ ⋊ C₂×C₅×C₉
Hall	C₅×C₇×#4294 ⋊ C₂
Hall	C₅×D₁₃₃ ⋊ C₉
Hall	C₇×#4294 ⋊ C₂×C₅
Hall	C₅×#4294 ⋊ D₇
Hall	C₅×C₇×C₁₉ ⋊ C₂×C₉
Hall	D₁₃₃ ⋊ C₅×C₉
Hall	#4294 ⋊ C₅×D₇
Hall	C₅×C₁₉ ⋊ C₉×D₇
Hall	C₅×C₇ ⋊ #4294⋊C₂
Sylow	C₁₉ ⋊ C₅×C₉×D₇
Sylow	C₇ ⋊ C₅×#4294⋊C₂

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₅	(C₁₉⋊C₃)⋊D₇
commutator, hypocenter	C₇×C₁₉	C₂×C₅×C₉
Frattini	C₃	C₅×(C₁₉⋊C₃)⋊D₇
Fitting, socle	C₃×C₅×C₇×C₁₉	C₂×C₃
prime radical	C₃×C₅×D₁₃₃	C₃
cosocle	C₃×C₇×C₁₉	C₂×C₃×C₅
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₃×C₅

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

540 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₇×#4294⋊C₂, D₅×#4294⋊D₇, (C₅⋊(#4294⋊C₂))⋊D₇, …
maximal normal subgroup of	C₅×D₇×#4294⋊C₂, D₅×#4294⋊D₇, (C₅⋊(#4294⋊C₂))⋊D₇, …
maximal quotient of	C₅×#4294⋊Dic₇, C₂×C₅×#4294⋊D₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 29);