Finite Group Databasebeta

C2×#13092139 #15671673

order2944
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#13092139

Splittings

SylowC23 ⋊ C2×#322

Subgroups

subgroupG/H
centerC2×C42C2×D23
commutatorC2×C23C2×C4×C8
FrattiniC42C22×D23
FittingC2×C4×C8×C23C2
socle, prime radicalC23×C23C42
cosocleC42×C23C23
hypercenterC2×C4×C8D23
hypocenterC23C2×#322
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C42 ◁ C2×C4×C8

248 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 173 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2786);