Finite Group Databasebeta

C2×#21444271 #29646610

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21444271

Splittings

FittingC22×C4×C8×C61 ⋊ C2
SylowC61 ⋊ C2×#1492

Subgroups

subgroupG/H
centerC22×C4C2×D244
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC22×C4×C8×C61C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840312C2
cosocleC42×C61C24
hypercenterC22×C4×C8D61
hypocenterC61C2×#1492
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×C8

1430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

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, 136165);