Finite Group Databasebeta

← Prev (#63319) Next (#63321) →

C₄×D₃₅ #63320

order	280
isoclinism	isoclinic class of D₃₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

C₄×D₃₅

Splittings

Fitting	C₄×C₅×C₇ ⋊ C₂
derived, Hall	C₅×C₇ ⋊ C₂×C₄
Sylow	C₇ ⋊ C₄×D₅
Sylow	C₅ ⋊ C₄×D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₄	D₃₅
commutator, hypocenter	C₅×C₇	C₂×C₄
Frattini	C₂	C₂×D₃₅
Fitting	C₄×C₅×C₇	C₂
socle, cosocle	C₂×C₅×C₇	C₂²
prime radical	C₂×D₃₅	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₄

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 140

A minimal faithful permutation representation — 2 generators on 16 points:

(2,3)(4,5)(6,7)(9,10)(11,12);(1,2,4,6,7,5,3)(8,9,11,12,10)(13,14,15,16)

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10587837, #10587840, C₈×D₃₅, …
maximal normal subgroup of	#10587837, #10587840, C₈×D₃₅, …
maximal quotient of	C₈×D₃₅, #10587893, C₄×Dic₃₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(280, 25);