Finite Group Databasebeta

C22×#16839633 #29838317

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC22×#16839633

Splittings

FittingC23×C4⋊C4×C61 ⋊ C2
SylowC61 ⋊ C22×#385

Subgroups

subgroupG/H
centerC25C22×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC23×C4⋊C4×C61C2
socleC25×C61C23
prime radicalC25×D61C22
cosocleC23×C61C25
hypercenterC23×C4⋊C4D61
hypocenterC61C22×#385
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C25 ◁ C23×C4⋊C4

8670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 327872);