Finite Group Databasebeta

C2×C22⋊C16×D61 #29832676

order15616
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C27

Aliases

direct productC2×C22⋊C16×D61

Splittings

FittingC2×C61×C22⋊C16 ⋊ C2
SylowC61 ⋊ C22×C22⋊C16

Subgroups

subgroupG/H
centerC22×C8C22×D61
commutatorC2×C61C23×C16
FrattiniC2×C8C23×D61
FittingC2×C61×C22⋊C16C2
socleC23×C61C22×C8
prime radicalC24×D61C8
cosocleC2×C8×C61C24
hypercenterC2×C22⋊C16D61
hypocenterC61C22×C22⋊C16
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C8 ◁ C2×C22⋊C16

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 322231);