Finite Group Databasebeta

C2×#21436208 #29465280

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

Aliases

direct productC2×#21436208

Splittings

FittingC2×C59×#417 ⋊ C2
SylowC59 ⋊ C2×#3316

Subgroups

subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#417C2
socleC23×C59C22×D4
prime radicalC2×#16838059C2
hypercenterC2×#417D59
hypocenterC59C2×#3316
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

2158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1334 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1046159);