C₂⁴×D₈₃₉ #41001606

order	26848
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

direct product	C₂⁴×D₈₃₉
unambiguous semidirect product	C₈₃₉⋊C₂⁵
unambiguous semidirect product	(C₂×C₈₃₉)⋊C₂⁴

Fitting, socle	C₂⁴×C₈₃₉ ⋊ C₂
derived, Sylow	C₈₃₉ ⋊ C₂⁵

	subgroup	G/H
center, hypercenter	C₂⁴	D₈₃₉
commutator, cosocle, hypocenter	C₈₃₉	C₂⁵
Frattini	C₁	G
Fitting, socle	C₂⁴×C₈₃₉	C₂
LCS	G ▷ C₈₃₉
UCS	C₁ ◁ C₂⁴

748 conjugacy classes of subgroups.

μ_t(G) = 13424

6736 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26848, 195);