Finite Group Databasebeta

C2×#13092183 #15673126

order2944
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13092183

Splittings

SylowC23 ⋊ C2×#342

Subgroups

subgroupG/H
centerC23(C2×D23)⋊C4
commutatorC22×C23C2×C42
FrattiniC24C22×D23
FittingC22×C22⋊C4×C23C2
socleC23×C23C22⋊C4
prime radicalC25×C23C22
cosocleC24×C23C23
hypercenterC22×C22⋊C4D23
hypocenterC23C2×#342
LCSG ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

680 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, 4239);