Finite Group Databasebeta

C2×#21436305 #29465495

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21436305

Splittings

FittingC2×C59×#452 ⋊ C2
SylowC59 ⋊ C2×#3323

Subgroups

subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#452C2
socleC23×C59C22×D4
prime radicalC2×#16838040C2
hypercenterC2×#452D59
hypocenterC59C2×#3323
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

2254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1046374);