Finite Group Databasebeta

← Prev (#19099391) Next (#19099393) →

H(5,𝔽₂)×D₇₉ #19099392

order	5056
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹

Aliases

H(5,𝔽₂)×D₇₉

Splittings

Fitting	H(5,𝔽₂)×C₇₉ ⋊ C₂
Sylow	C₇₉ ⋊ C₂×H(5,𝔽₂)

Subgroups

	subgroup	G/H
center, Frattini	C₂	C₂⁴×D₇₉
commutator, socle	C₂×C₇₉	C₂⁵
Fitting	H(5,𝔽₂)×C₇₉	C₂
hypercenter	H(5,𝔽₂)	D₇₉
hypocenter	C₇₉	C₂×H(5,𝔽₂)
LCS	G ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ H(5,𝔽₂)

898 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

697 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5056, 1378);