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C₁₅₇×D₁₃⋊C₉ #49145000

order	36738
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₅₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₅₇×D₁₃⋊C₉
unambiguous semidirect product	D₁₃⋊(C₉×C₁₅₇)
unambiguous semidirect product	(C₁₃⋊C₉)⋊(C₂×C₁₅₇)

Splittings

derived, Sylow	C₁₃ ⋊ C₂×C₉×C₁₅₇
Hall	C₁₃⋊C₉×C₁₅₇ ⋊ C₂
Hall	D₁₃×C₁₅₇ ⋊ C₉
Hall	C₁₃×C₁₅₇ ⋊ C₂×C₉
Hall	C₁₃⋊C₉ ⋊ C₂×C₁₅₇
Hall	D₁₃ ⋊ C₉×C₁₅₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₅₇	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂×C₉×C₁₅₇
Frattini	C₃	D₁₃⋊C₃×C₁₅₇
Fitting, socle	C₃×C₁₃×C₁₅₇	C₂×C₃
prime radical	C₃×D₁₃×C₁₅₇	C₃
cosocle	C₃×C₁₃	C₂×C₃×C₁₅₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₁₅₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 18369

Conjugacy classes & character table

3768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36738, 23);