C₂×D₂₉₅ #11924381

order	1180
isoclinism	isoclinic class of D₂₉₅
automorphism	Aut(G) order 136880
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₅₉₀
direct product	C₂×D₂₉₅
unambiguous semidirect product	(C₂×C₅)⋊D₅₉
unambiguous semidirect product	(C₂×C₅₉)⋊D₅

Splittings

Fitting, socle	C₂×C₅×C₅₉ ⋊ C₂
derived, Hall	C₅×C₅₉ ⋊ C₂²
Sylow	C₅₉ ⋊ C₂×D₅
Sylow	C₅ ⋊ C₂×D₅₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₂₉₅
commutator, cosocle, hypocenter	C₅×C₅₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₅₉	C₂
LCS	G ▷ C₅×C₅₉
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 66
transitive degree	μ_t(G) = 590

A minimal faithful permutation representation — 2 generators on 66 points:

(1,2)(3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66);(4,7)(5,6)(9,66)(10,65)(11,64)(12,63)(13,62)(14,61)(15,60)(16,59)(17,58)(18,57)(19,56)(20,55)(21,54)(22,53)(23,52)(24,51)(25,50)(26,49)(27,48)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₃×D₂₉₅, C₂×D₈₈₅, C₂×C₃×D₂₉₅, …
maximal normal subgroup of	C₂×C₃×D₂₉₅, C₂×C₁₁×D₂₉₅, C₂×C₁₃×D₂₉₅, …
maximal quotient of	D₃×D₂₉₅, C₂×D₈₈₅, C₂×C₃×D₂₉₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1180, 10);

C2×D295 #11924381