Finite Group Databasebeta

C2×#13092167 #15672137

order2944
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#13092167

Splittings

SylowC23 ⋊ C2×#334

Subgroups

subgroupG/H
centerC22×C4C22⋊D23
commutatorC4×C23C22×C8
FrattiniC42C22×D23
FittingC2×C23×C4⋊C8C2
socle, prime radicalC23×C23C4⋊C4
cosocleC42×C23C23
hypercenterC2×C4⋊C8D23
hypocenterC23C2×#334
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊C8

200 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 125 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 3250);