C₃²×D₅×C₃₄₉ #44536121

order	31410
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₃₄₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×D₅×C₃₄₉
unambiguous semidirect product	C₅⋊(C₂×C₃²×C₃₄₉)

	subgroup	G/H
center, hypercenter	C₃²×C₃₄₉	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃²×C₃₄₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₃₄₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃²×C₃₄₉

48 conjugacy classes of subgroups.

μ_t(G) = 15705

12564 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31410, 23);