Finite Group Databasebeta

C2×#21443716 #29570238

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

Aliases

direct productC2×#21443716

Splittings

SylowC61 ⋊ C2×#1301

Subgroups

subgroupG/H
centerC22×C4#11758198
commutatorC2×C4×C61C2×C42
FrattiniC2×C42C22×D61
FittingC22×C4⋊C8×C61C2
socleC23×C61#95
prime radicalC24×C61C4⋊C4
cosocleC2×C42×C61C23
hypercenterC22×C4⋊C8D61
hypocenterC61C2×#1301
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4⋊C8

666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2476 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 59793);