Finite Group Databasebeta

C2×#21434963 #29459359

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21434963

Splittings

FittingC2×C59×#536 ⋊ C2
SylowC59 ⋊ C2×#3200

Subgroups

subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#536C2
socleC23×C59C22×D4
prime radicalC2×#16837966C2
hypercenterC2×#536D59
hypocenterC59C2×#3200
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#536

2314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1328 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1040238);