Finite Group Databasebeta

C2×#21424206 #28588551

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21424206

Splittings

FittingC2×C59×#344 ⋊ C2
SylowC59 ⋊ C2×#1829

Subgroups

subgroupG/H
centerC22#16837264
commutatorC23×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#344C2
socleC22×C59#381
prime radicalC23×D236C22
cosocleC22×C4×C59C24
hypercenterC2×#344D59
hypocenterC59C2×#1829
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

1434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 169430);