Finite Group Databasebeta

C22×#16840710 #30624570

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C212

Aliases

direct productC22×#16840710
unambiguous semidirect productD61⋊(C2×#386)

Splittings

FittingC23×D4×C61 ⋊ C4
SylowC61 ⋊ C22×#386

Subgroups

subgroupG/H
centerC24C22×#6923
commutatorC22×C61C24×C4
FrattiniC22C24×#6923
FittingC23×D4×C61C4
socleC24×C61C22×C4
prime radicalC23×D4×D61C2
cosocleC22×D61C25
hypercenterC23×D4#6923
hypocenterC61C22×#386
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×D4

11630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1114125);