C₂×C₇×C₁₉×D₅₇ #44476733

order	30324
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₇×C₁₉×D₅₇
unambiguous semidirect product	(C₂×C₃)⋊(C₇×C₁₉×D₁₉)
unambiguous semidirect product	(C₂×C₁₉)⋊(D₃×C₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₉	D₅₇
commutator, cosocle, hypocenter	C₃×C₁₉	C₂²×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₉²	C₂
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×C₇×C₁₉

152 conjugacy classes of subgroups.

μ_t(G) = 1596

7980 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30324, 316);