Finite Group Databasebeta

C22×#16840754 #30625189

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×#16840754
unambiguous semidirect productD61⋊(C2×#418)

Splittings

FittingC23×D4×C61 ⋊ C4
SylowC61 ⋊ C22×#418

Subgroups

subgroupG/H
centerC23C2×C22⋊#6923
commutatorC4×C61C24×C4
FrattiniC4C24×#6923
FittingC23×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D4×D61C2
cosocleC4×D61C25
hypercenterC23×D4#6923
hypocenterC61C22×#418
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D4

7214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1114744);