Finite Group Databasebeta

C2×#21443925 #29594928

order15616
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21443925

Splittings

SylowC61 ⋊ C2×#1386

Subgroups

subgroupG/H
centerC23#14519699
commutatorC8×C61C2×C42
FrattiniC22×C8C22×D61
FittingC22×M32×C61C2
socleC23×C61#102
prime radicalC24×C61D8
cosocleC22×C8×C61C23
hypercenterC22×M32D61
hypocenterC61C2×#1386
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2464 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 84483);