Finite Group Databasebeta

C2×#13092262 #15675723

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

Aliases

direct productC2×#13092262

Splittings

SylowC23 ⋊ C2×#376

Subgroups

subgroupG/H
centerC24C22×D23
commutatorC2×C23C22×C42
FrattiniC23C23×D23
FittingC2×C23×#95C2
socle, prime radicalC24×C23C23
cosocleC23×C23C24
hypercenterC2×#95D23
hypocenterC23C2×#376
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C24 ◁ C2×#95

840 conjugacy classes of subgroups; only the 405 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 405 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 6836);