Finite Group Databasebeta

C2×#21428366 #28758454

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

Aliases

direct productC2×#21428366

Splittings

FittingC22×#117×C59 ⋊ C2
SylowC59 ⋊ C2×#2482

Subgroups

subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC22×#117×C59C2
socleC24×C59C24
prime radicalC25×D59C22
hypercenterC22×#117D59
hypocenterC59C2×#2482
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×#117

4166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2396 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 339333);