Finite Group Databasebeta

C4×#16840117 #29687998

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

Aliases

direct productC4×#16840117

Splittings

FittingC42×C8×C61 ⋊ C2
SylowC61 ⋊ C4×#488

Subgroups

subgroupG/H
centerC22×C4C2×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC42×C8×C61C2
socleC23×C61C22×D4
prime radicalC22×D244C23
cosocleC22×C4×C61C24
hypercenterC42×C8D61
hypocenterC61C4×#488
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C43 ◁ C42×C8

858 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

3928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 177553);