Finite Group Databasebeta

C2×#21447307 #29709050

order15616
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21447307

Splittings

SylowC61 ⋊ C2×#2086

Subgroups

subgroupG/H
centerC24C2×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×C4⋊C8×C61C2
socle, prime radicalC24×C61C2×D4
hypercenterC22×C4⋊C8D61
hypocenterC61C2×#2086
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊C8

1054 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15616

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, 198605);