Finite Group Databasebeta

← Prev (#45691685) Next (#45691687) →

C₁₉×C₉⋊#5997 #45691686

order	33516
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₁₉×C₉⋊#5997
unambiguous semidirect product	C₉⋊(C₁₉×#5997)

Splittings

Fitting, Hall	C₇²×C₉×C₁₉ ⋊ C₄
derived, Hall	C₇²×C₉ ⋊ C₄×C₁₉
Hall	C₇²×C₁₉ ⋊ Dic₉
Hall	C₉×C₁₉ ⋊ #5997
Sylow	C₇² ⋊ C₁₉×Dic₉
Sylow	C₉ ⋊ C₁₉×#5997

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	C₉⋊#5997
commutator, hypocenter	C₇²×C₉	C₄×C₁₉
Frattini	C₃	C₁₉×C₃⋊#5997
Fitting	C₇²×C₉×C₁₉	C₄
socle	C₃×C₇²×C₁₉	Dic₃
prime radical	C₃×C₁₉×C₇⋊D₇	D₃
cosocle	C₉×C₇⋊D₇	C₂×C₁₉
LCS	G ▷ C₇²×C₉
UCS	C₁ ◁ C₁₉

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2394

Conjugacy classes & character table

2280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 484);