Finite Group Databasebeta

C2×#21437389 #29495398

order15104
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#21437389

Splittings

FittingC2×C4×#41×C59 ⋊ C2
SylowC59 ⋊ C2×#3444

Subgroups

subgroupG/H
centerC2×C42C22×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C4×#41×C59C2
socleC23×C59C25
hypercenterC2×C4×#41D59
hypocenterC59C2×#3444
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C42 ◁ C2×C4×#41

8518 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076277);