Finite Group Databasebeta

C2×#21437197 #29495156

order15104
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC2×#21437197

Splittings

FittingC2×C59×#504 ⋊ C2
SylowC59 ⋊ C2×#3407

Subgroups

subgroupG/H
centerC2×C8C23×D59
commutatorC2×C59C24×C8
FrattiniC8C24×D59
FittingC2×C59×#504C2
socleC22×C59C23×C8
prime radicalC2×#41×D59C4
cosocleC8×C59C25
hypercenterC2×#504D59
hypocenterC59C2×#3407
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C8 ◁ C2×#504

2074 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2456 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076035);