Finite Group Databasebeta

C2×#13092522 #15682182

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

Aliases

direct productC2×#13092522

Splittings

SylowC23 ⋊ C2×#441

Subgroups

subgroupG/H
centerC23C2×C22⋊D23
commutatorC4×C23C23×C4
FrattiniC2×C4C23×D23
FittingC2×C4×Q8×C23C2
socle, prime radicalC23×C23C2×D4
cosocleC2×C4×C23C24
hypercenterC2×C4×Q8D23
hypocenterC23C2×#441
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

480 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 205 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 13295);