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#37613161

order	24738
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₇×C₁₉×C₃₁ ⋊ C₂×C₃
Hall	#27136504 ⋊ C₂
Hall	D₇×C₁₉×C₃₁ ⋊ C₃
Hall	C₁₉×C₃₁ ⋊ AGL(1,𝔽₇)
Hall	D₇×C₃₁ ⋊ C₁₉⋊C₃
Hall	D₇×C₁₉ ⋊ C₃₁⋊C₃
Hall	C₇×C₃₁ ⋊ C₂×C₁₉⋊C₃
Hall	C₇×C₁₉ ⋊ C₂×C₃₁⋊C₃
Sylow	C₃₁ ⋊ #11716326
Sylow	C₁₉ ⋊ #13049958
Hall	D₇ ⋊ #13183715
Sylow	C₇ ⋊ C₂×#13183715

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₉×C₃₁	C₂×C₃
LCS	G ▷ C₇×C₁₉×C₃₁
UCS	C₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4123

Polycyclic presentation:

2,3,7,19,31|c^a=c^6,c^b=c^2,d^b=d^11,e^b=e^5

Conjugacy classes & character table

987 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24738, 81);