Finite Group Databasebeta

C2×#92030 #11757039

order960
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#92030

Splittings

HallC3×C5 ⋊ C2×2−1+4
SylowC5 ⋊ C2×#1007
SylowC3 ⋊ C2×#4150

Subgroups

subgroupG/H
centerC22C22×D3×D5
commutator, cosocleC2×C3×C5C25
FrattiniC2C23×D3×D5
FittingC2×C3×C5×Q8C22
socleC22×C3×C5C24
hypercenterC2×Q8D3×D5
hypocenterC3×C5C2×2−1+4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

1588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#14297410, #14412035, #14412216, …
maximal normal subgroup of#14297410, #14412035, #14412216, …
maximal quotient ofC2×#11753405, C2×#11755140, C2×#11755124, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 11234);