Finite Group Databasebeta

C2×#13092157 #15671978

order2944
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#13092157

Splittings

SylowC23 ⋊ C2×#329

Subgroups

subgroupG/H
centerC23C22⋊Dic23
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC2×C23×#124C2
socleC23×C23C22⋊C4
prime radicalC22×D4×C23C4
cosocleC42×C23C23
hypercenterC2×#124D23
hypocenterC23C2×#329
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

284 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 93 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) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 3091);