Finite Group Databasebeta

C2×#21437182 #29469717

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

Aliases

direct productC2×#21437182

Splittings

FittingC2×C4×D8×C59 ⋊ C2
SylowC59 ⋊ C2×#3403

Subgroups

subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C4×D8×C59C2
socleC23×C59C22×D4
hypercenterC2×C4×D8D59
hypocenterC59C2×#3403
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

2066 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1682 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1050596);