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C₂×D₇×#4294 #18012115

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

Aliases

C₂×D₇×#4294

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₇×C₁₉⋊C₃
commutator, hypocenter	C₇×C₁₉	C₂²×C₉
Frattini	C₃	C₂×D₇×C₁₉⋊C₃
Fitting, socle	C₂×C₃×C₇×C₁₉	C₂×C₃
prime radical	C₂×C₃×D₇×C₁₉	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

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

Relationships

maximal subgroup of	D₅×D₇×#4294, C₂×C₅×D₇×#4294, C₂×D₃₅×#4294, …
maximal normal subgroup of	C₂×C₅×D₇×#4294, C₂×C₇×D₇×#4294
maximal quotient of	D₅×D₇×#4294, C₂×C₅×D₇×#4294, C₂×D₃₅×#4294, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4788, 31);