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C₈×C₇⋊AGL(1,𝔽₅) #11764668

order	1120
isoclinism	isoclinic class of C₇⋊AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₄×C₈ · Schur multiplier (H₂) = C₄

Aliases

C₈×C₇⋊AGL(1,𝔽₅)

Splittings

Fitting	C₅×C₇×C₈ ⋊ C₄
derived, Hall	C₅×C₇ ⋊ C₄×C₈
Sylow	C₇ ⋊ C₈×AGL(1,𝔽₅)
Sylow	C₅ ⋊ C₈×Dic₇

Subgroups

	subgroup	G/H
center, hypercenter	C₈	C₇⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₇	C₄×C₈
Frattini	C₄	C₂×C₇⋊AGL(1,𝔽₅)
Fitting	C₅×C₇×C₈	C₄
socle	C₂×C₅×C₇	C₄²
prime radical	C₂×C₇×D₅	C₂×C₄
cosocle	C₄×C₇×D₅	C₂²
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₈

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 280

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₉)×C₇⋊AGL(1,𝔽₅), C₈×ΓL(1,𝔽₈)⋊AGL(1,𝔽₅), C₈×D₇×AGL(1,𝔽₅), …
maximal normal subgroup of	C₈×ΓL(1,𝔽₈)⋊AGL(1,𝔽₅), C₈×D₇×AGL(1,𝔽₅), M₁₆×C₇⋊AGL(1,𝔽₅), …
maximal quotient of	AGL(1,𝔽₉)×C₇⋊AGL(1,𝔽₅)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 274);