C₇×D₁₄₃₅ #34095605

order	20090
automorphism	?
homology	Abelianization (H₁) = C₂×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₁₄₃₅
unambiguous semidirect product	C₅⋊(C₇×D₂₈₇)
unambiguous semidirect product	C₇⋊(C₇×D₂₀₅)
unambiguous semidirect product	C₄₁⋊(C₇×D₃₅)

Splittings

Fitting, socle, Hall	C₅×C₇²×C₄₁ ⋊ C₂
derived	C₅×C₇×C₄₁ ⋊ C₂×C₇
Hall	C₇²×C₄₁ ⋊ D₅
Hall	C₅×C₇² ⋊ D₄₁
Hall	C₅×C₄₁ ⋊ C₇×D₇
Sylow	C₇² ⋊ D₂₀₅
Sylow	C₄₁ ⋊ C₇×D₃₅
Sylow	C₅ ⋊ C₇×D₂₈₇

Subgroups

	subgroup	G/H
center, hypercenter	C₇	D₁₄₃₅
commutator, cosocle, hypocenter	C₅×C₇×C₄₁	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₄₁	C₂
LCS	G ▷ C₅×C₇×C₄₁
UCS	C₁ ◁ C₇

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 2870

A minimal faithful permutation representation — 2 generators on 60 points:

(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)(50,51)(52,53)(54,55)(57,58)(59,60);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(49,50,52,54,55,53,51)(56,57,59,60,58)

Conjugacy classes & character table

5033 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20090, 28);

C7×D1435 #34095605