Finite Group Databasebeta

C2×#21437229 #29495192

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#21437229

Splittings

FittingC2×C59×#508 ⋊ C2
SylowC59 ⋊ C2×#3414

Subgroups

subgroupG/H
centerC2×C4D8×D59
commutator, cosocleC8×C59C25
FrattiniC8C24×D59
FittingC2×C59×#508C2
socleC22×C59C22×D8
hypercenterC2×#508D59
hypocenterC59C2×#3414
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#508

2098 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076071);