Finite Group Databasebeta

C4×#16839485 #29570516

order15616
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#16839485

Splittings

FittingC4×C22⋊C8×C61 ⋊ C2
SylowC61 ⋊ C4×#323

Subgroups

subgroupG/H
centerC22×C4#11758198
commutatorC22×C61C2×C4×C8
FrattiniC23×C4C22×D61
FittingC4×C22⋊C8×C61C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC23×C4×C61C23
hypercenterC4×C22⋊C8D61
hypocenterC61C4×#323
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2488 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 60071);