C₇⋊D₇×C₃₇₉ #49151012

order	37142
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₇₉ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₇⋊D₇×C₃₇₉
unambiguous semidirect product	C₇⋊(D₇×C₃₇₉)

Fitting, socle, Hall	C₇²×C₃₇₉ ⋊ C₂
derived, Sylow	C₇² ⋊ C₂×C₃₇₉

	subgroup	G/H
center, hypercenter	C₃₇₉	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂×C₃₇₉
Frattini	C₁	G
Fitting, socle	C₇²×C₃₇₉	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃₇₉

40 conjugacy classes of subgroups.

μ_t(G) = 18571

9854 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37142, 15);