Finite Group Databasebeta

C22×#16839491 #29646356

order15616
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC22×#16839491

Splittings

FittingC22×C4×C8×C61 ⋊ C2
SylowC61 ⋊ C22×D4⋊C8

Subgroups

subgroupG/H
centerC23×C4D244
commutatorC4×C61C23×C8
FrattiniC42C23×D61
FittingC22×C4×C8×C61C2
socleC24×C61C22⋊C4
prime radicalC23×D244C4
cosocleC42×C61C24
hypercenterC22×C4×C8D61
hypocenterC61C22×D4⋊C8
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×C8

1886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

3952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 135911);