C₅×D₇×C₃₄₉ #37567693

order	24430
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₃₄₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₇×C₃₄₉
unambiguous semidirect product	C₇⋊(C₂×C₅×C₃₄₉)

	subgroup	G/H
center, hypercenter	C₅×C₃₄₉	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₅×C₃₄₉
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₃₄₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₅×C₃₄₉

16 conjugacy classes of subgroups.

μ_t(G) = 12215

8725 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24430, 3);