Finite Group Databasebeta

C2×#21425337 #28616365

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

Aliases

direct productC2×#21425337

Splittings

FittingC2×C59×#389 ⋊ C2
SylowC59 ⋊ C2×#2042

Subgroups

subgroupG/H
centerC24C2×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#389C2
socleC24×C59C2×D4
prime radicalC23×D236C22
hypercenterC2×#389D59
hypocenterC59C2×#2042
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

1670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 197244);