Finite Group Databasebeta

C4×#16839787 #29677898

order15616
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#16839787

Splittings

FittingC4×C4⋊C8×C61 ⋊ C2
SylowC61 ⋊ C4×#424

Subgroups

subgroupG/H
centerC2×C42C22×D61
commutatorC22×C61C22×C42
FrattiniC22×C4C23×D61
FittingC4×C4⋊C8×C61C2
socleC23×C61C23×C4
prime radicalC23×D61C22×C4
cosocleC22×C4×C61C24
hypercenterC4×C4⋊C8D61
hypocenterC61C4×#424
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C42 ◁ C4×C4⋊C8

1174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 167453);