C₅²⋊C₃×C₃₄₉ #39908696

order	26175
automorphism	?
homology	Abelianization (H₁) = C₃×C₃₄₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²⋊C₃×C₃₄₉
unambiguous semidirect product	C₅²⋊(C₃×C₃₄₉)

Fitting, socle, Hall	C₅²×C₃₄₉ ⋊ C₃
derived, Sylow	C₅² ⋊ C₃×C₃₄₉

	subgroup	G/H
center, hypercenter	C₃₄₉	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₃×C₃₄₉
Frattini	C₁	G
Fitting, socle	C₅²×C₃₄₉	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃₄₉

12 conjugacy classes of subgroups.

μ_t(G) = 5235

3839 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26175, 4);