Finite Group Databasebeta

← Prev (#49181534) Next (#49181536) →

C₉×D₇×C₄₃⋊C₇ #49181535

order	37926
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₇×C₄₃⋊C₇
unambiguous semidirect product	(C₉×D₇×C₄₃)⋊C₇

Splittings

Fitting	C₇×C₉×C₄₃ ⋊ C₂×C₇
derived	C₇×C₄₃ ⋊ C₂×C₇×C₉
Hall	C₇×C₉×C₄₃⋊C₇ ⋊ C₂
Hall	C₇×C₄₃⋊C₇ ⋊ C₂×C₉
Hall	C₉×C₄₃ ⋊ C₇×D₇
Sylow	C₄₃ ⋊ C₇×C₉×D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₇×C₄₃⋊C₇
commutator, hypocenter	C₇×C₄₃	C₂×C₇×C₉
Frattini	C₃	C₃×D₇×C₄₃⋊C₇
Fitting	C₇×C₉×C₄₃	C₂×C₇
socle, cosocle	C₃×C₇×C₄₃	C₂×C₃×C₇
prime radical	C₃×D₇×C₄₃⋊C₇	C₃
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₉

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2709

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37926, 108);