C₁₇×ΓL(1,𝔽₈)×C₈₉ #44540978

order	31773
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₇×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×ΓL(1,𝔽₈)×C₈₉
unambiguous semidirect product	C₇⋊(C₃×C₁₇×C₈₉)
unambiguous semidirect product	(C₇×C₁₇)⋊(C₃×C₈₉)
unambiguous semidirect product	(C₇×C₈₉)⋊(C₃×C₁₇)
unambiguous semidirect product	(C₇×C₁₇×C₈₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₁₇×C₈₉	ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇	C₃×C₁₇×C₈₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₇×C₈₉	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₁₇×C₈₉

16 conjugacy classes of subgroups.

μ_t(G) = 10591

7565 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31773, 2);