Finite Group Databasebeta

C4×#10625100 #15675919

order2944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#10625100

Splittings

FittingC22×C42×C23 ⋊ C2
SylowC23 ⋊ C4×#123

Subgroups

subgroupG/H
centerC22×C4C22×D23
commutatorC22×C23C23×C4
FrattiniC23C23×D23
FittingC22×C42×C23C2
socle, cosocleC23×C23C24
prime radicalC22×C22⋊D23C22
hypercenterC22×C42D23
hypocenterC23C4×#123
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ C22×C42

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 7032);