C₇⋊D₇×C₂₃₉ #37552823

order	23422
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₃₉ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₇⋊D₇×C₂₃₉
unambiguous semidirect product	C₇⋊(D₇×C₂₃₉)

Fitting, socle, Hall	C₇²×C₂₃₉ ⋊ C₂
derived, Sylow	C₇² ⋊ C₂×C₂₃₉

	subgroup	G/H
center, hypercenter	C₂₃₉	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂×C₂₃₉
Frattini	C₁	G
Fitting, socle	C₇²×C₂₃₉	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂₃₉

40 conjugacy classes of subgroups.

μ_t(G) = 11711

6214 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23422, 15);