C₇×A₄×C₁₃×C₂₃ #38737446

order	25116
automorphism	?
homology	Abelianization (H₁) = C₃×C₇×C₁₃×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×A₄×C₁₃×C₂₃
unambiguous semidirect product	C₂²⋊(C₃×C₇×C₁₃×C₂₃)
unambiguous semidirect product	(C₂²×C₂₃)⋊(C₃×C₇×C₁₃)

	subgroup	G/H
center, hypercenter	C₇×C₁₃×C₂₃	A₄
commutator, cosocle, hypocenter	C₂²	C₃×C₇×C₁₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₂²×C₇×C₁₃×C₂₃	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₇×C₁₃×C₂₃

40 conjugacy classes of subgroups.

μ_t(G) = 8372

8372 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 165);