C₇×C₁₉×C₂₉⋊C₇ #41008838

order	26999
automorphism	?
homology	Abelianization (H₁) = C₇²×C₁₉ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₇×C₁₉×C₂₉⋊C₇
unambiguous semidirect product	C₂₉⋊(C₇²×C₁₉)
unambiguous semidirect product	(C₇×C₂₉)⋊(C₇×C₁₉)
unambiguous semidirect product	(C₁₉×C₂₉)⋊C₇²
unambiguous semidirect product	(C₇×C₁₉×C₂₉)⋊C₇

	subgroup	G/H
center, hypercenter	C₇×C₁₉	C₂₉⋊C₇
commutator, cosocle, hypocenter	C₂₉	C₇²×C₁₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₉×C₂₉	C₇
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₇×C₁₉

40 conjugacy classes of subgroups.

μ_t(G) = 3857

1463 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26999, 4);