Finite Group Databasebeta

C22×#16839716 #30543403

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

Aliases

direct productC22×#16839716

Splittings

FittingC22×C4×C8×C61 ⋊ C2
SylowC61 ⋊ C22×#405

Subgroups

subgroupG/H
centerC23×C8C2×D61
commutatorC2×C61C23×C42
FrattiniC2×C4C24×D61
FittingC22×C4×C8×C61C2
socleC24×C61C22×C4
prime radicalC24×D61C2×C4
cosocleC2×C4×C61C25
hypercenterC22×C4×C8D61
hypocenterC61C22×#405
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C23×C8 ◁ C22×C4×C8

3518 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

4000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1032958);