C₅²⋊C₃×C₃₇₉ #43249407

order	28425
automorphism	?
homology	Abelianization (H₁) = C₃×C₃₇₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²⋊C₃×C₃₇₉
unambiguous semidirect product	C₅²⋊(C₃×C₃₇₉)

Fitting, socle, Hall	C₅²×C₃₇₉ ⋊ C₃
derived, Sylow	C₅² ⋊ C₃×C₃₇₉

	subgroup	G/H
center, hypercenter	C₃₇₉	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₃×C₃₇₉
Frattini	C₁	G
Fitting, socle	C₅²×C₃₇₉	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃₇₉

12 conjugacy classes of subgroups.

μ_t(G) = 5685

4169 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28425, 4);