Finite Group Databasebeta

C4×#10625078 #15681821

order2944
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#10625078

Splittings

FittingC4×M16×C23 ⋊ C2
SylowC23 ⋊ C4×#131

Subgroups

subgroupG/H
centerC42C22×D23
commutatorC2×C23C22×C42
FrattiniC2×C4C23×D23
FittingC4×M16×C23C2
socleC22×C23C23×C4
prime radicalC2×#67288C22
cosocleC2×C4×C23C24
hypercenterC4×M16D23
hypocenterC23C4×#131
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C42 ◁ C4×M16

572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 12934);