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C₂×#4294⋊D₇ #18012116

order	4788
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×#4294⋊D₇
unambiguous semidirect product	(C₂×#4294)⋊D₇

Splittings

derived, Hall	C₇×C₁₉ ⋊ C₂²×C₉
Hall	C₇×#4294 ⋊ C₂²
Hall	C₂×D₁₃₃ ⋊ C₉
Hall	#4294 ⋊ C₂×D₇
Sylow	C₁₉ ⋊ C₂×C₉×D₇
Sylow	C₇ ⋊ C₂×#4294⋊C₂

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₁₉⋊C₃)⋊D₇
commutator, hypocenter	C₇×C₁₉	C₂²×C₉
Frattini	C₃	C₂×(C₁₉⋊C₃)⋊D₇
Fitting, socle	C₂×C₃×C₇×C₁₉	C₂×C₃
prime radical	C₂×C₃×D₁₃₃	C₃
cosocle	C₃×C₇×C₁₉	C₂²×C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₂×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2394

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₅×#4294⋊D₇, C₂×C₅×#4294⋊D₇, C₂×C₅⋊(#4294⋊D₇), …
maximal normal subgroup of	C₂×C₅×#4294⋊D₇, C₂×C₇×#4294⋊D₇
maximal quotient of	D₅×#4294⋊D₇, C₂×C₅×#4294⋊D₇, C₂×C₅⋊(#4294⋊D₇), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4788, 32);