Finite Group Databasebeta

C22×#16839831 #30543849

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#16839831

Splittings

FittingC23×M16×C61 ⋊ C2
SylowC61 ⋊ C22×#435

Subgroups

subgroupG/H
centerC23×C4C22×D61
commutatorC22×C61C24×C4
FrattiniC2×C4C24×D61
FittingC23×M16×C61C2
socleC24×C61C22×C4
prime radicalC23×C22⋊D61C4
cosocleC2×C4×C61C25
hypercenterC23×M16D61
hypocenterC61C22×#435
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C23×M16

3350 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, 1033404);