Finite Group Databasebeta

C2×#21425355 #28616477

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

Aliases

direct productC2×#21425355

Splittings

FittingC22×#101×C59 ⋊ C2
SylowC59 ⋊ C2×#2046

Subgroups

subgroupG/H
centerC23#14273700
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC22×#101×C59C2
socleC23×C59#121
prime radicalC23×D236C22
hypercenterC22×#101D59
hypocenterC59C2×#2046
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#101

1458 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, 197356);