Finite Group Databasebeta

C23×(C2×#6923)⋊C4 #30624535

order15616
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C212

Aliases

direct productC23×(C2×#6923)⋊C4
unambiguous semidirect productD61⋊(C22×#95)

Splittings

FittingC24×C4×C61 ⋊ C4
SylowC61 ⋊ C23×#95

Subgroups

subgroupG/H
centerC25C2×#6923
commutatorC2×C61C23×C42
FrattiniC22C24×#6923
FittingC24×C4×C61C4
socleC25×C61C2×C4
prime radicalC25×D61C22
cosocleC22×D61C25
hypercenterC24×C4#6923
hypocenterC61C23×#95
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C25 ◁ C24×C4

14334 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, 1114090);