Finite Group Databasebeta

C2×#346×D59 #28741313

order15104
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#346×D59

Splittings

FittingC2×C59×#346 ⋊ C2
SylowC59 ⋊ C22×#346

Subgroups

subgroupG/H
centerC22×C8C22×D59
commutatorC2×C59C22×C4×C8
FrattiniC2×C8C23×D59
FittingC2×C59×#346C2
socleC23×C59C22×C8
prime radicalC23×D59C2×C8
cosocleC2×C8×C59C24
hypercenterC2×#346D59
hypocenterC59C22×#346
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C2×#346

942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322192);