Finite Group Databasebeta

C2×#21424505 #28590303

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21424505

Splittings

SylowC59 ⋊ C2×#1889

Subgroups

subgroupG/H
centerC23#14273695
commutatorC23×C59C23×C4
FrattiniC24C23×D59
Fitting, prime radicalC22×#120×C59C2
socleC23×C59#120
cosocleC24×C59C24
hypercenterC22×#120D59
hypocenterC59C2×#1889
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C25 ◁ C22×#120

3566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 171182);