D₃²×C₇×C₈₉ #36375916

order	22428
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₈₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃²×C₇×C₈₉
unambiguous semidirect product	(C₃×D₃)⋊(C₂×C₇×C₈₉)
unambiguous semidirect product	(C₃⋊D₃)⋊(C₂×C₇×C₈₉)

	subgroup	G/H
center, hypercenter	C₇×C₈₉	D₃²
commutator, cosocle, hypocenter	C₃²	C₂²×C₇×C₈₉
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₈₉	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₇×C₈₉

88 conjugacy classes of subgroups.

μ_t(G) = 3738

5607 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22428, 98);