Finite Group Databasebeta

C2×#21433445 #29455317

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#21433445

Splittings

FittingC2×C59×#585 ⋊ C2
SylowC59 ⋊ C2×#3018

Subgroups

subgroupG/H
centerC2×C4#14273696
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#585C2
socleC22×C59C2×#120
hypercenterC2×#585D59
hypocenterC59C2×#3018
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#585

4850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

2036 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1036196);