Finite Group Databasebeta

C2×#21449594 #29848039

order15616
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21449594

Splittings

SylowC61 ⋊ C2×#2446

Subgroups

subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#387C2
socle, prime radicalC24×C61C24
hypercenterC2×#387D61
hypocenterC61C2×#2446
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#387

2550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15616

Conjugacy classes & character table

1756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 337594);