Finite Group Databasebeta

C2×#21449515 #29847840

order15616
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#21449515

Splittings

SylowC61 ⋊ C2×#2440

Subgroups

subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC23×C4⋊C4×C61C2
socleC24×C61C24
prime radicalC25×C61C23
hypercenterC23×C4⋊C4D61
hypocenterC61C2×#2440
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4⋊C4

3550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2476 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 337395);