Finite Group Databasebeta

C2×#21425735 #28741408

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21425735

Splittings

FittingC2×C59×#410 ⋊ C2
SylowC59 ⋊ C2×#2120

Subgroups

subgroupG/H
centerC2×C4#14273641
commutatorC23×C59C23×C4
FrattiniC2×D4C23×D59
FittingC2×C59×#410C2
socleC22×C59C2×#99
prime radicalC2×#16837909C2
cosocleC2×D4×C59C24
hypercenterC2×#410D59
hypocenterC59C2×#2120
LCSG ▷ C23×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

1398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1328 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322287);