Finite Group Databasebeta

C2×#21437238 #29495203

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#21437238

Splittings

FittingC22×SD32×C59 ⋊ C2
SylowC59 ⋊ C2×#3416

Subgroups

subgroupG/H
centerC22C2×D8×D59
commutator, cosocleC8×C59C25
FrattiniC8C24×D59
FittingC22×SD32×C59C2
socleC22×C59C22×D8
hypercenterC22×SD32D59
hypocenterC59C2×#3416
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

2074 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076082);