C₅²⋊C₃×C₃₉₇ #44446769

order	29775
automorphism	?
homology	Abelianization (H₁) = C₃×C₃₉₇ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²⋊C₃×C₃₉₇
unambiguous semidirect product	C₅²⋊(C₃×C₃₉₇)

Fitting, socle, Hall	C₅²×C₃₉₇ ⋊ C₃
derived, Sylow	C₅² ⋊ C₃×C₃₉₇

	subgroup	G/H
center, hypercenter	C₃₉₇	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₃×C₃₉₇
Frattini	C₁	G
Fitting, socle	C₅²×C₃₉₇	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃₉₇

12 conjugacy classes of subgroups.

μ_t(G) = 5955

4367 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29775, 4);