Finite Group Databasebeta

← Prev (#45691963) Next (#45691965) →

C₇²×C₁₉×C₃⋊Dic₃ #45691964

order	33516
automorphism	?
homology	Abelianization (H₁) = C₄×C₇²×C₁₉ · Schur multiplier (H₂) = C₃×C₇

Aliases

direct product	C₇²×C₁₉×C₃⋊Dic₃
unambiguous semidirect product	C₃⋊(C₇²×Dic₃×C₁₉)

Splittings

derived, Sylow	C₃² ⋊ C₄×C₇²×C₁₉
Hall	C₃²×C₇²×C₁₉ ⋊ C₄
Hall	C₃²×C₇² ⋊ C₄×C₁₉
Hall	C₃²×C₁₉ ⋊ C₄×C₇²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₇²×C₁₉	C₃⋊D₃
commutator, hypocenter	C₃²	C₄×C₇²×C₁₉
Frattini	C₂	C₇²×C₃⋊D₃×C₁₉
Fitting, socle, prime radical	C₂×C₃²×C₇²×C₁₉	C₂
cosocle	C₂×C₃²	C₂×C₇²×C₁₉
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₇²×C₁₉

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 33516

Conjugacy classes & character table

11172 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 762);