Finite Group Databasebeta

C23×C22⋊C4×D61 #30586563

order15616
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C216

Aliases

direct productC23×C22⋊C4×D61

Splittings

FittingC23×C22⋊C4×C61 ⋊ C2
SylowC61 ⋊ C24×C22⋊C4

Subgroups

subgroupG/H
centerC25C22×D61
commutatorC2×C61C25×C4
FrattiniC22C25×D61
FittingC23×C22⋊C4×C61C2
socleC25×C61C23
prime radicalC26×D61C2
cosocleC22×C61C26
hypercenterC23×C22⋊C4D61
hypocenterC61C24×C22⋊C4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C25 ◁ C23×C22⋊C4

43678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1076118);