Finite Group Databasebeta

C2×#21427382 #28754961

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

Aliases

direct productC2×#21427382

Splittings

FittingC2×C59×#376 ⋊ C2
SylowC59 ⋊ C2×#2398

Subgroups

subgroupG/H
centerC23×C4C22×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#376C2
socleC24×C59C24
prime radicalC23×D236C22
hypercenterC2×#376D59
hypocenterC59C2×#2398
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C2×#376

3246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 335840);