C₄₁×D₃₅ #15668285

order	2870
isoclinism	isoclinic class of D₃₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₁×D₃₅
unambiguous semidirect product	C₅⋊(D₇×C₄₁)
unambiguous semidirect product	C₇⋊(D₅×C₄₁)

Splittings

Fitting, socle, Hall	C₅×C₇×C₄₁ ⋊ C₂
derived, Hall	C₅×C₇ ⋊ C₂×C₄₁
Hall	C₇×C₄₁ ⋊ D₅
Hall	C₅×C₄₁ ⋊ D₇
Sylow	C₇ ⋊ D₅×C₄₁
Sylow	C₅ ⋊ D₇×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₄₁	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂×C₄₁
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₄₁	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₄₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1435

A minimal faithful permutation representation — 2 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41)(42,43,44,45,46)(47,48,49,50,51,52,53);(43,46)(44,45)(48,53)(49,52)(50,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₁×D₁₇₅, D₃₅×C₄₁⋊C₅, C₄₁×C₅⋊D₃₅, …
maximal normal subgroup of	D₃₅×C₄₁⋊C₅, C₅×C₄₁×D₃₅, C₇×C₄₁×D₃₅, …
maximal quotient of	C₄₁×D₁₇₅, C₄₁×C₅⋊D₃₅, C₅×C₄₁×D₃₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2870, 8);

C41×D35 #15668285