C₂×C₃×C₂₉×ΓL(1,𝔽₃₂) #41004183

order	26970
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₃×C₂₉×ΓL(1,𝔽₃₂)
unambiguous semidirect product	(C₂×C₃×C₃₁)⋊(C₅×C₂₉)
unambiguous semidirect product	(C₂×C₃×C₂₉×C₃₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₉	ΓL(1,𝔽₃₂)
commutator, cosocle, hypocenter	C₃₁	C₂×C₃×C₅×C₂₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₂₉×C₃₁	C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₃×C₂₉

32 conjugacy classes of subgroups.

μ_t(G) = 5394

1914 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26970, 2);