C₇²×D₂₇₁ #40997887

order	26558
automorphism	?
homology	Abelianization (H₁) = C₂×C₇² · Schur multiplier (H₂) = C₇

Aliases

direct product	C₇²×D₂₇₁
unambiguous semidirect product	C₂₇₁⋊(C₂×C₇²)

Fitting, socle, Hall	C₇²×C₂₇₁ ⋊ C₂
derived, Sylow	C₂₇₁ ⋊ C₂×C₇²

	subgroup	G/H
center, hypercenter	C₇²	D₂₇₁
commutator, cosocle, hypocenter	C₂₇₁	C₂×C₇²
Frattini	C₁	G
Fitting, socle	C₇²×C₂₇₁	C₂
LCS	G ▷ C₂₇₁
UCS	C₁ ◁ C₇²

40 conjugacy classes of subgroups.

μ_t(G) = 13279

6713 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26558, 6);