Finite Group Databasebeta

C4×#16840485 #29839972

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#16840485

Splittings

FittingC42×Q8×C61 ⋊ C2
SylowC61 ⋊ C4×#556

Subgroups

subgroupG/H
centerC22×C4C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC42×Q8×C61C2
socle, cosocleC23×C61C25
prime radicalC22×D244C23
hypercenterC42×Q8D61
hypocenterC61C4×#556
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C42×Q8

2340 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 329527);