Finite Group Databasebeta

C2×#21448177 #29838229

order15616
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#21448177

Splittings

FittingC22×#95×C61 ⋊ C2
SylowC61 ⋊ C2×#2275

Subgroups

subgroupG/H
centerC24C23×D61
commutatorC2×C61C23×C42
FrattiniC23C24×D61
FittingC22×#95×C61C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC22×#95D61
hypocenterC61C2×#2275
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×#95

4694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2536 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 327784);