C₃⁴×D₇ #11765815

order	1134
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃⁴ · Schur multiplier (H₂) = C₃⁶

Aliases

C₃⁴×D₇

Fitting, socle, Hall	C₃⁴×C₇ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₃⁴

	subgroup	G/H
center, hypercenter	C₃⁴	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃⁴
Frattini	C₁	G
Fitting, socle	C₃⁴×C₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃⁴

848 conjugacy classes of subgroups.

μ_t(G) = 567

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1134, 245);