C₇⋊D₇×C₃₈₃ #49176236

order	37534
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₈₃ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₇⋊D₇×C₃₈₃
unambiguous semidirect product	C₇⋊(D₇×C₃₈₃)

Fitting, socle, Hall	C₇²×C₃₈₃ ⋊ C₂
derived, Sylow	C₇² ⋊ C₂×C₃₈₃

	subgroup	G/H
center, hypercenter	C₃₈₃	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂×C₃₈₃
Frattini	C₁	G
Fitting, socle	C₇²×C₃₈₃	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃₈₃

40 conjugacy classes of subgroups.

μ_t(G) = 18767

9958 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37534, 9);