Finite Group Databasebeta

C22×#16839564 #29832886

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×#16839564

Splittings

FittingC23×C16×C61 ⋊ C2
SylowC61 ⋊ C22×#357

Subgroups

subgroupG/H
centerC24D488
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC23×C16×C61C2
socleC24×C61D8
prime radicalC23×D488C2
cosocleC2×C8×C61C24
hypercenterC23×C16D61
hypocenterC61C22×#357
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8 ◁ C23×C16

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

3928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 322441);