Finite Group Databasebeta

C2×#21426050 #28742609

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21426050

Splittings

FittingC2×C59×#509 ⋊ C2
SylowC59 ⋊ C2×#2192

Subgroups

subgroupG/H
centerC22#16837534
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC2×C59×#509C2
socleC22×C59#447
hypercenterC2×#509D59
hypocenterC59C2×#2192
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

1150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 323488);