C₇⋊D₇×C₂₂₉ #36376271

order	22442
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₂₉ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₇⋊D₇×C₂₂₉
unambiguous semidirect product	C₇⋊(D₇×C₂₂₉)

Fitting, socle, Hall	C₇²×C₂₂₉ ⋊ C₂
derived, Sylow	C₇² ⋊ C₂×C₂₂₉

	subgroup	G/H
center, hypercenter	C₂₂₉	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂×C₂₂₉
Frattini	C₁	G
Fitting, socle	C₇²×C₂₂₉	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂₂₉

40 conjugacy classes of subgroups.

μ_t(G) = 11221

5954 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22442, 9);