Finite Group Databasebeta

C2×#21434311 #29456953

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

Aliases

direct productC2×#21434311

Splittings

SylowC59 ⋊ C2×#3120

Subgroups

subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#452C2
socleC23×C59C22×D4
prime radicalC22×#41×C59C22
hypercenterC2×#452D59
hypocenterC59C2×#3120
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

2070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1166 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1037832);