Finite Group Databasebeta

C2×#21448019 #29834802

order15616
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21448019

Splittings

SylowC61 ⋊ C2×#2236

Subgroups

subgroupG/H
centerC23C2×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#467C2
socleC23×C61C2×D8
prime radicalC24×C61D8
hypercenterC2×#467D61
hypocenterC61C2×#2236
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#467

630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

1378 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 324357);