C₂×D₉₃₅ #16836700

order	3740
automorphism	Aut(G) order 1196800
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₈₇₀
direct product	C₂×D₉₃₅
unambiguous semidirect product	(C₂×C₅)⋊D₁₈₇
unambiguous semidirect product	(C₂×C₁₁)⋊D₈₅
unambiguous semidirect product	(C₂×C₁₇)⋊D₅₅

Splittings

Fitting, socle	C₂×C₅×C₁₁×C₁₇ ⋊ C₂
derived, Hall	C₅×C₁₁×C₁₇ ⋊ C₂²
Hall	C₁₁×C₁₇ ⋊ C₂×D₅
Hall	C₅×C₁₇ ⋊ C₂×D₁₁
Hall	C₅×C₁₁ ⋊ C₂×D₁₇
Sylow	C₁₇ ⋊ C₂×D₅₅
Sylow	C₁₁ ⋊ C₂×D₈₅
Sylow	C₅ ⋊ C₂×D₁₈₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₉₃₅
commutator, cosocle, hypocenter	C₅×C₁₁×C₁₇	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁×C₁₇	C₂
LCS	G ▷ C₅×C₁₁×C₁₇
UCS	C₁ ◁ C₂

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1870

A minimal faithful permutation representation — 2 generators on 35 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);(4,7)(5,6)(9,18)(10,17)(11,16)(12,15)(13,14)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₃×D₉₃₅, C₂×D₂₈₀₅, C₂×C₃×D₉₃₅, …
maximal normal subgroup of	C₂×C₃×D₉₃₅, C₂×C₅⋊(C₁₇⋊AGL(1,𝔽₁₁)), C₂×C₅×D₉₃₅, …
maximal quotient of	D₃×D₉₃₅, C₂×D₂₈₀₅, C₂×C₃×D₉₃₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3740, 46);

C2×D935 #16836700