Finite Group Databasebeta

C22×D61⋊(C22⋊C8) #30625125

order15616
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C211

Aliases

direct productC22×D61⋊(C22⋊C8)
unambiguous semidirect productD61⋊(C22×C22⋊C8)

Splittings

SylowC61 ⋊ C23×C22⋊C8

Subgroups

subgroupG/H
centerC23×C4C2×#6923
commutatorC2×C61C24×C8
FrattiniC22C24×#6923
FittingC24×C4×C61C4
socleC24×C61C22×C4
prime radicalC25×D61C4
cosocleC2×Dic61C25
hypercenterC24×C4#6923
hypocenterC61C23×C22⋊C8
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C24×C4

7646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1114680);