Finite Group Databasebeta

C2×#13092834 #15686496

order2944
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13092834

Splittings

SylowC23 ⋊ C2×#504

Subgroups

subgroupG/H
centerC2×C8C22×D23
commutatorC2×C23C23×C8
FrattiniC8C23×D23
FittingC2×C23×#131C2
socleC22×C23C22×C8
prime radicalC2×#41×C23C4
cosocleC8×C23C24
hypercenterC2×#131D23
hypocenterC23C2×#504
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C8 ◁ C2×#131

368 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, 17609);