Finite Group Databasebeta

C4×#16839813 #29678139

order15616
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#16839813

Splittings

FittingC42×C8×C61 ⋊ C2
SylowC61 ⋊ C4×#431

Subgroups

subgroupG/H
centerC43C2×D61
commutatorC2×C61C22×C4×C8
FrattiniC22×C4C23×D61
FittingC42×C8×C61C2
socleC23×C61C23×C4
prime radicalC23×D61C22×C4
cosocleC22×C4×C61C24
hypercenterC42×C8D61
hypocenterC61C4×#431
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C43 ◁ C42×C8

1318 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, 167694);