Finite Group Databasebeta

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C₇×C₉×D₄₃⋊C₇ #49181533

order	37926
automorphism	?
homology	Abelianization (H₁) = C₂×C₇²×C₉ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₇×C₉×D₄₃⋊C₇
unambiguous semidirect product	(C₉×D₄₃)⋊C₇²
unambiguous semidirect product	(C₇×C₉×D₄₃)⋊C₇

Splittings

Fitting	C₇×C₉×C₄₃ ⋊ C₂×C₇
derived, Sylow	C₄₃ ⋊ C₂×C₇²×C₉
Hall	C₇×C₉×C₄₃⋊C₇ ⋊ C₂
Hall	C₇×C₄₃⋊C₇ ⋊ C₂×C₉
Hall	C₉×D₄₃ ⋊ C₇²
Hall	C₉×C₄₃ ⋊ C₂×C₇²
Hall	D₄₃ ⋊ C₇²×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₉	D₄₃⋊C₇
commutator, hypocenter	C₄₃	C₂×C₇²×C₉
Frattini	C₃	C₃×C₇×D₄₃⋊C₇
Fitting	C₇×C₉×C₄₃	C₂×C₇
socle	C₃×C₇×C₄₃	C₂×C₃×C₇
prime radical	C₃×C₇×D₄₃⋊C₇	C₃
cosocle	C₃×C₄₃	C₂×C₃×C₇²
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₇×C₉

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2709

Conjugacy classes & character table

1071 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37926, 106);