Finite Group Databasebeta

C2×#21445556 #29677457

order15616
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC2×#21445556

Splittings

FittingC2×C61×#343 ⋊ C2
SylowC61 ⋊ C2×#1742

Subgroups

subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C61C22×C42
FrattiniC22×C4C23×D61
FittingC2×C61×#343C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC22×C4×C61C24
hypercenterC2×#343D61
hypocenterC61C2×#1742
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

2190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 167012);