Finite Group Databasebeta

C2×#21423451 #28570918

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

Aliases

direct productC2×#21423451

Splittings

FittingC2×C8×D4×C59 ⋊ C2
SylowC59 ⋊ C2×#1667

Subgroups

subgroupG/H
centerC23#14273701
commutator, cosocleC42×C59C24
FrattiniC42C23×D59
FittingC2×C8×D4×C59C2
socleC23×C59#121
hypercenterC2×C8×D4D59
hypocenterC59C2×#1667
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C8×D4

958 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2378 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 151797);