Finite Group Databasebeta

C2×#21426084 #28742695

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21426084

Splittings

SylowC59 ⋊ C2×#2197

Subgroups

subgroupG/H
centerC22#16837588
commutator, cosocleC2×D4×C59C24
FrattiniC2×D4C23×D59
Fitting, prime radicalC2×C59×B(4,𝔽2)C2
socleC22×C59B(4,𝔽2)
hypercenterC2×B(4,𝔽2)D59
hypocenterC59C2×#2197
LCSG ▷ C2×D4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×B(4,𝔽2)

1320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 323574);