Finite Group Databasebeta

C2×#13092433 #15681938

order2944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13092433

Splittings

FittingC22×M16×C23 ⋊ C2
SylowC23 ⋊ C2×#421

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊D23
commutatorC4×C23C23×C4
FrattiniC2×C4C23×D23
FittingC22×M16×C23C2
socleC22×C23C2×C22⋊C4
prime radicalC22×#67288C2
cosocleC2×C4×C23C24
hypercenterC22×M16D23
hypocenterC23C2×#421
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 736

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 13051);