Finite Group Databasebeta

C2×#21446707 #29683954

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#21446707

Splittings

FittingC22×C4×C8×C61 ⋊ C2
SylowC61 ⋊ C2×#1974

Subgroups

subgroupG/H
centerC22×C4C2×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×C4×C8×C61C2
socleC23×C61C4×D4
prime radicalC22×#14519799C2
cosocleC22×C4×C61C24
hypercenterC22×C4×C8D61
hypocenterC61C2×#1974
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C22×C4×C8

1558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

3928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 173509);