C₇×C₄₇×C₃⋊D₁₅ #44444124

order	29610
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₄₇ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₇×C₄₇×C₃⋊D₁₅
unambiguous semidirect product	C₃⋊(C₇×D₁₅×C₄₇)
unambiguous semidirect product	C₅⋊(C₇×C₃⋊D₃×C₄₇)

	subgroup	G/H
center, hypercenter	C₇×C₄₇	C₃⋊D₁₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂×C₇×C₄₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₄₇	C₂
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₇×C₄₇

96 conjugacy classes of subgroups.

μ_t(G) = 14805

7896 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29610, 61);