Finite Group Databasebeta

← Prev (#45691524) Next (#45691526) →

C₄×C₁₉×#89205 #45691525

order	33516
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₉ · Schur multiplier (H₂) = C₇

Aliases

C₄×C₁₉×#89205

Splittings

derived, Sylow	C₇² ⋊ C₄×C₉×C₁₉
Hall	C₄×C₇²×C₁₉ ⋊ C₉
Hall	C₇²×C₁₉ ⋊ C₄×C₉
Hall	C₄×C₇² ⋊ C₉×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄×C₁₉	#3862
commutator, hypocenter	C₇²	C₄×C₉×C₁₉
Frattini	C₂×C₃	C₂×C₁₉×#3862
Fitting	C₃×C₄×C₇²×C₁₉	C₃
socle, prime radical	C₂×C₃×C₇²×C₁₉	C₂×C₃
cosocle	C₂×C₃×C₇²	C₂×C₃×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₄×C₁₉

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4788

Conjugacy classes & character table

4332 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 323);