Finite Group Databasebeta

C2×#21426894 #28747592

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21426894

Splittings

SylowC59 ⋊ C2×#2336

Subgroups

subgroupG/H
centerC24C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC2×C59×#389C2
socle, prime radicalC24×C59C24
cosocleC23×C59C25
hypercenterC2×#389D59
hypocenterC59C2×#2336
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#389

2310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

1712 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 328471);