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#44443306

order	29526
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₇×C₁₉×C₃₇ ⋊ C₂×C₃
Hall	#28414268 ⋊ C₂
Hall	C₇×C₁₉×D₃₇ ⋊ C₃
Hall	C₁₉×D₃₇ ⋊ ΓL(1,𝔽₈)
Hall	C₁₉×C₃₇ ⋊ C₂×ΓL(1,𝔽₈)
Hall	C₇×D₃₇ ⋊ C₁₉⋊C₃
Hall	C₇×C₃₇ ⋊ C₂×C₁₉⋊C₃
Hall	C₇×C₁₉ ⋊ D₃₇⋊C₃
Hall	D₃₇ ⋊ #87704
Sylow	C₃₇ ⋊ C₂×#87704
Sylow	C₁₉ ⋊ #13095532
Sylow	C₇ ⋊ #16862423

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₉×C₃₇	C₂×C₃
LCS	G ▷ C₇×C₁₉×C₃₇
UCS	C₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4921

Polycyclic presentation:

2,3,7,19,37|e^a=e^36,c^b=c^2,d^b=d^7,e^b=e^10

Conjugacy classes & character table

892 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29526, 39);