Finite Group Databasebeta

C2×#21425318 #28616322

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

Aliases

direct productC2×#21425318

Splittings

FittingC2×C59×#417 ⋊ C2
SylowC59 ⋊ C2×#2039

Subgroups

subgroupG/H
centerC23#14273695
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#417C2
socleC23×C59#120
prime radicalC2×#16837980C2
hypercenterC2×#417D59
hypocenterC59C2×#2039
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

1586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 197201);