Finite Group Databasebeta

C22×#16840755 #30625190

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#16840755
unambiguous semidirect productD61⋊(C2×#419)

Splittings

FittingC23×Q8×C61 ⋊ C4
SylowC61 ⋊ C22×#419

Subgroups

subgroupG/H
centerC23C2×C22⋊#6923
commutatorC4×C61C24×C4
FrattiniC4C24×#6923
FittingC23×Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×D61D4
cosocleC4×D61C25
hypercenterC23×Q8#6923
hypocenterC61C22×#419
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q8

5070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

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, 1114745);