Finite Group Databasebeta

← Prev (#49136231) Next (#49136233) →

C₅₃×C₂²⋊#4294 #49136232

order	36252
automorphism	?
homology	Abelianization (H₁) = C₉×C₅₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅₃×C₂²⋊#4294
unambiguous semidirect product	C₂²⋊(C₅₃×#4294)
unambiguous semidirect product	(C₂²×C₅₃)⋊#4294

Splittings

derived, Hall	C₂²×C₁₉ ⋊ C₉×C₅₃
Hall	C₂²×C₁₉×C₅₃ ⋊ C₉
Hall	C₁₉×C₅₃ ⋊ C₂²⋊C₉
Hall	C₂²×C₅₃ ⋊ #4294
Sylow	C₁₉ ⋊ C₂²⋊C₉×C₅₃
Sylow	C₂² ⋊ C₅₃×#4294

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₅₃	C₂²⋊(C₁₉⋊C₃)
commutator, hypocenter	C₂²×C₁₉	C₉×C₅₃
Frattini	C₃	C₅₃×C₂²⋊(C₁₉⋊C₃)
Fitting, socle, prime radical	C₂²×C₃×C₁₉×C₅₃	C₃
cosocle	C₂²×C₃×C₁₉	C₃×C₅₃
LCS	G ▷ C₂²×C₁₉
UCS	C₁ ◁ C₃×C₅₃

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 18126

Conjugacy classes & character table

4452 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 31);