ΓL(1,𝔽₈)×C₄₁⋊C₂₅ #36340276

order	21525
automorphism	?
homology	Abelianization (H₁) = C₃×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	ΓL(1,𝔽₈)×C₄₁⋊C₂₅
unambiguous semidirect product	C₇⋊(C₃×C₄₁⋊C₂₅)
unambiguous semidirect product	C₄₁⋊(ΓL(1,𝔽₈)×C₂₅)
unambiguous semidirect product	(ΓL(1,𝔽₈)×C₄₁)⋊C₂₅
unambiguous semidirect product	(C₇×C₄₁⋊C₂₅)⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₅	ΓL(1,𝔽₈)×C₄₁⋊C₅
commutator, hypocenter	C₇×C₄₁	C₃×C₂₅
Fitting, socle, cosocle	C₅×C₇×C₄₁	C₃×C₅
prime radical	C₅×ΓL(1,𝔽₈)×C₄₁	C₅
LCS	G ▷ C₇×C₄₁
UCS	C₁ ◁ C₅

24 conjugacy classes of subgroups.

μ_t(G) = 7175

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21525, 4);