Finite Group Databasebeta

C2×#13092323 #15675866

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

Aliases

direct productC2×#13092323

Splittings

SylowC23 ⋊ C2×#391

Subgroups

subgroupG/H
centerC24C22×D23
commutatorC22×C23C23×C4
FrattiniC23C23×D23
FittingC22×C42×C23C2
socle, prime radicalC24×C23C23
cosocleC23×C23C24
hypercenterC22×C42D23
hypocenterC23C2×#391
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C24 ◁ C22×C42

928 conjugacy classes of subgroups; only the 381 normal subgroups are shown.

normal subgroups only

This group has 928 conjugacy classes of subgroups — too many to draw. Only its 381 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2944

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, 6979);